If you use our software for your research, we would be grateful if you could cite one or more of the following papers.
C. D. Cantwell, D. Moxey, A. Comerford, A. Bolis, G. Rocco, G. Mengaldo, D. De Grazia, S. Yakovlev, J-E. Lombard, D. Ekelschot, B. Jordi, H. Xu, Y. Mohamied, C. Eskilsson, B. Nelson, P. Vos, C. Biotto, R. M. Kirby, and S. J. Sherwin, “Nektar++: An open-source spectral/hp element framework,” Computer physics communications, vol. 192, pp. 205-219, 2015.
D. Moxey, C. D. Cantwell, Y. Bao, A. Cassinelli, G. Castiglioni, S. Chun, E. Juda, E. Kazemi, K. Lackhove, J. Marcon, G. Mengaldo, D. Serson, M. Turner, H. Xu, J. Peiró, R. M. Kirby, S. J. Sherwin, “Nektar++: enhancing the capability and application of high-fidelity spectral/hp element methods”, Computer physics communications, vol. 249, 107110, 2020
This helps demonstrate impact to funding agencies and supports further development of the code.
Below is a list of publications which describe the developments in, or application of, Nektar++. If you have published a paper using Nektar++, please submit it using the instructions here, to include it on this page.
Core numerical methods
2025
- A. I. Liosi, H. Wüstenberg, P. Khurana, S. Sherwin, J. Hoessler, A. Swift and A. Chatzopoulosin AIAA SCITECH 2025 Forum, 2025. doi 10.2514/6.2025-1486BiBTeX Abstract
@inbook{2025:liosi.wustenberg.ea:comparing, author = {Liosi, Alexandra I. and W{\"u}stenberg, Henrik and Khurana, Parv and Sherwin, Spencer and Hoessler, Julien and Swift, Adam and Chatzopoulos, Athanasios}, title = {Comparing Efficient Implicit Time-Stepping Techniques for Highly Resolved Simulations Using Industrial Geometries}, year = {2025}, booktitle = {AIAA SCITECH 2025 Forum}, doi = {10.2514/6.2025-1486}, groups = {core}, url = {https://arc.aiaa.org/doi/abs/10.2514/6.2025-1486}, eprint = {https://arc.aiaa.org/doi/pdf/10.2514/6.2025-1486} }High-fidelity modeling approaches such as LES are increasingly used for analyzing complex, unsteady flow phenomena in industrial geometries at high Reynolds numbers. However, their computational cost prevents widespread adoption as a standard tool in developing aerodynamic devices. One potential solution is to increase the simulation time step, even beyond the CFL limit, when employing implicit schemes to discretize the equations. Two implicit time-stepping techniques for solving the incompressible Navier-Stokes equations in a segregated manner using the high-order Spectral h/p element method were examined in this study. Our objectives were to explore the stability margins for each scheme, assess their impact on accuracy, and evaluate the achieved speed-up. The Imperial Front Wing (IFW) industrial benchmark was considered for these purposes. Both schemes successfully allowed for an increased simulation timestep, resulting in a considerable reduction in the total computation time. As the timestep increased, the flow accuracy deviated more from the reference simulation. This work outlines the characteristics of each scheme, compares them with existing literature on canonical flows, and highlights the trade-offs between accuracy and computational efficiency. - M. Lahooti, E. Laughton, J. Ye, C. D. Cantwell and D. MoxeyBiBTeX AbstractDiscontinuous Galerkin simulation of sliding geometries using a point-to-point interpolation techniqueJournal of Computational Physics, 524, p. 113734, 2025. doi 10.1016/j.jcp.2025.113734
@article{2025:lahooti.laughton.ea:discontinuous, author = {Lahooti, M. and Laughton, E. and Ye, J. and Cantwell, C. D. and Moxey, D.}, title = {Discontinuous Galerkin simulation of sliding geometries using a point-to-point interpolation technique}, journal = {Journal of Computational Physics}, year = {2025}, volume = {524}, pages = {113734}, groups = {core}, doi = {10.1016/j.jcp.2025.113734}, issn = {0021-9991} }The high-fidelity modelling of geometry which rotates or translates is a key requirement in fluid mechanics applications, enabling the simulation of parts such as rotors and pressure cascades. These prescribed motions can be imposed through the movement of the mesh representing the problem, where an interface is constructed across the nonconformal interface, bridging the static and moving regions of the mesh. The challenge is maintaining the solution accuracy across this interface, which will involve nonconformal elements on its sides due to the sliding meshes, while having a robust and efficient approach for complex interfaces. This work uses a point-to-point interpolation technique for such sliding interfaces, leveraging the high-order discontinuous Galerkin method for discretising governing equations and the Arbitrary Lagrangian-Eulerian (ALE) method in handling sliding meshes. With its straightforward and efficient approach, the point-to-point interpolation method has an advantage over other approaches in dealing with the complex interface while having excellent accuracy in preserving the discrete geometric conservation law (DGCL), as demonstrated in this study. Linear and non-linear hyperbolic systems, including the compressible Euler and Navier-Stokes equations, are considered with detailed analysis demonstrating the point-to-point method’s accuracy using several examples and under various settings in the context of high-order methods for flow problems.
2024
- R. C. Moura, L. D. Fernandes, A. F. C. da Silva and S. J. SherwinBiBTeX AbstractJoint-mode diffusion analysis of spectral/hp continuous Galerin Methods: Towards superior dissipation estimates for implicit LESComputer Methods in Applied Mechanics and Engineering, 2024. doi 10.1016/j.cma.2024.117025
@article{2024:moura.l-d-fernandes.ea:joint-mode, author = {Moura, R.C. and Fernandes, L.D. and da Silva, A.F. C. and Sherwin, S. J.}, title = {Joint-mode diffusion analysis of spectral/hp continuous Galerin Methods: Towards superior dissipation estimates for implicit LES}, journal = {Computer Methods in Applied Mechanics and Engineering}, year = {2024}, doi = {10.1016/j.cma.2024.117025}, groups = {core} }We present a new linear eigensolution analysis technique that provides superior estimates of dissipation distribution in wavenumber space for the continuous Galerkin (CG) method. The technique builds upon traditional dispersion-diffusion analyses that have been applied to spectral/hp element methods, but in particular is an improvement upon the non-modal eigenanalysis approach proposed by Fernandez et al. (2019). The present technique takes into account the indirect effects that dispersion may have on dissipation, as recently discussed by Moura et al. (2022), in order to better represent dissipation itself. Also, a concept used by the dynamic mode decomposition (DMD) community is invoked to weight the relative contribution of the multiple diffusion curves that stem from temporal eigenanalysis. This allows for obtaining a single dissipation profile in wavenumber space, so that the proposed technique is named joint-mode analysis. Although the non-modal approach also provides a single diffusion curve, the joint-mode dissipation curve is shown to correlate significantly better with the energy spectrum of Burgers’ turbulence at large and intermediate scales, which is particularly relevant for implicit large-eddy simulation (LES). The proposed technique is readily extensible to other spectral/hp element methods. - K. S. Kirilov, J. Peiró, M. D. Green, D. Moxey, L. Veiga, F. Dassi and A. RussoBiBTeXCurvilinear Mesh Generation for the High-Order Virtual Element Method (VEM)2024, pp. 419–439. doi 10.1007/978-3-031-40594-5_19
@inproceedings{2024:kirilov.peiro.ea:curvilinear, author = {Kirilov, Kaloyan S and Peir\'o, Joaquim and Green, Mashy D and Moxey, David and Veiga, Lourenco and Dassi, Franco and Russo, Alessandro}, title = {Curvilinear Mesh Generation for the High-Order Virtual Element Method (VEM)}, year = {2024}, pages = {419--439}, month = mar, groups = {core}, doi = {10.1007/978-3-031-40594-5_19} } - P. Khurana, S. J. Sherwin, J. Hoessler, D. Moxey and A. Chatzopoulosin Robust and Scalable Solvers in HPC: Recent Developments and Future Challenges, 2024. doi 10.23967/eccomas.2024.280BiBTeX Abstract
@inproceedings{2024:khurana.sherwin.ea:lower-order, author = {Khurana, Parv and Sherwin, Spencer J. and Hoessler, Julien and Moxey, David and Chatzopoulos, Athanasios}, title = {Lower-order Refined preconditioning for spectral/hp element methods for complex, 3D geometries}, booktitle = {Robust and Scalable Solvers in HPC: Recent Developments and Future Challenges}, year = {2024}, organization = {Scipedia}, groups = {core}, doi = {10.23967/eccomas.2024.280}, url = {https://www.scipedia.com/public/Khurana_et_al_2024a} }The current work presents the incorporation of the \textitLower-Order Refined (LOR) preconditioner within the incompressible Navier-Stokes equations solver of the open-source spectral/\textithp element method framework \nekpp. This preconditioner is constructed on a low-order (\textitP=1) finite element discretisation spectrally equivalent to a given high-order discretisation. The LOR preconditioner offers advantages such as low-cost operator evaluations, a constant memory requirement per degree of freedom, minimal sensitivity to high aspect-ratio elements, and a controlled iterative condition number with increasing problem size. The contribution extends to developing a functional LOR preconditioner tailored for mixed-element 3D mesh configurations, encompassing both prismatic and tetrahedral elements, allowing for the use of complex geometries that require unstructured 3D meshes with boundary layers. Notably, the \nekpp implementation is the first instance of using the LOR preconditioner with a modal expansion basis function. This study presents the iterative performance and scaling of the proposed preconditioner for solving the pressure Poisson system arising from the incompressible Navier-Stokes equations solver, using industrial test cases relevant to the context of race-car aerodynamics. - M. D. Green, K. S. Kirilov, M. Turner, J. Marcon, J. Eichstädt, E. Laughton, C. D. Cantwell, S. J. Sherwin, J. Peiró and D. MoxeyBiBTeX AbstractNekMesh: An open-source high-order mesh generation frameworkComputer Physics Communications, (298), p. 109089, 2024. doi 10.1016/j.cpc.2024.109089
@article{2024:green.kirilov.ea:nekmesh, author = {Green, M. D. and Kirilov, K. S. and Turner, M. and Marcon, J. and Eichst\"adt, J. and Laughton, E. and Cantwell, C. D. and Sherwin, S. J. and Peir\'o, J. and Moxey, D.}, title = {NekMesh: An open-source high-order mesh generation framework}, journal = {Computer Physics Communications}, year = {2024}, number = {298}, pages = {109089}, groups = {core}, doi = {10.1016/j.cpc.2024.109089} }High-order spectral element simulations are now becoming increasingly popular within the computational modelling community, as they offer the potential to deliver increased accuracy at reduced cost compared to traditional low-order codes. However, to support accurate, high-fidelity simulations in complex industrial applications, there is a need to generate curvilinear meshes which robustly and accurately conform to geometrical features. This is, at present, a key challenge within the mesh generation community, with only a few open-source tools able to generate curvilinear meshes for complex geometries. We present NekMesh: an open-source mesh generation package which is designed to enable the generation of valid, high-quality curvilinear meshes of complex, three-dimensional geometries for performing high-order simulations. We outline the software architecture adopted in NekMesh, which uses a pipeline of processing modules to provide a flexible, CAD-independent high-order mesh processing tool, capable of both generating meshes for a wide range of use cases, as well as post-processing linear meshes from a range of input formats for use with high-order simulations. A number of examples in various application areas are presented, with a particular emphasis on challenging aeronautical and fluid dynamics test cases.
2022
- G. Vivarelli, J. A. Isler, F. Montomoli, S. J. Sherwin and P. AdamiBiBTeX AbstractHigh-Order Spectral/hp Compressible and Incompressible Comparison of Transitional Boundary-Layers Subject to a Realistic Pressure Gradient and High Reynolds Numberin Turbo Expo: Power for Land, Sea, and Air, 2022, 86113, p. V10CT32A024. doi 10.1115/GT2022-82100
@inproceedings{2022:vivarelli.isler.ea:high-order, author = {Vivarelli, Guglielmo and Isler, Jo{\~a}o Anderson and Montomoli, Francesco and Sherwin, Spencer J and Adami, Paolo}, title = {High-Order Spectral/$hp$ Compressible and Incompressible Comparison of Transitional Boundary-Layers Subject to a Realistic Pressure Gradient and High $Reynolds$ Number}, booktitle = {Turbo Expo: Power for Land, Sea, and Air}, year = {2022}, volume = {86113}, pages = {V10CT32A024}, organization = {American Society of Mechanical Engineers}, groups = {core}, doi = {10.1115/GT2022-82100} }Within the literature, there are limited high-order results concerning large Reynolds number flows under the influence of strong adverse pressure gradients, mainly due to the computational expense involved. The main advantage in employing high-order methodologies over standard second-order finite-volume solvers, relates to their ability to increase accuracy with a significantly lower number of degrees of freedom. In theory, this would permit Direct Numerical Simulation sort of analysis. Yet, there is still a significant computational cost involved. For this reason, an efficient approach to analyse such flows by means of a Nektar++ high-order Implicit Large Eddy Simulation is proposed. The flow conditions considered in this case cause a separation bubble to form with consequent turbulent transition. In particular, Tollmien-Schlichting instabilities trigger Kelvin-Helmholtz behaviour, which in turn cause the turbulent transition. The bulk of the study will be carried out with the incompressible flow solver, as it is assumed that compressibility effects are negligible within the boundary layer. An initial 2D analysis will be conducted to determine the necessary spatial resolution and whether it is possible to consider a subset of the overall simulation domain to reduce the computational expense. Once this will have been established, the 3D results will be achieved by Fourier expansion in the cross-flow direction. These results will prove the cost-effectiveness of the methodology, that could be used within an industrial setting with a limited turn-around time. Additionally, a comparison between the results achieved by means of the Nektar++ compressible flow solver in 2D and 3D will be provided, to assess any differences that may be present. - M. W. Hess, A. Lario, G. Mengaldo and G. RozzaBiBTeX AbstractReduced order modeling for spectral element methods: current developments in Nektar++ and further perspectivesarXiv preprint arXiv:2201.05404, 2022. doi 10.48550/arXiv.2201.05404
@article{2022:hess.lario.ea:reduced, author = {Hess, Martin W and Lario, Andrea and Mengaldo, Gianmarco and Rozza, Gianluigi}, title = {Reduced order modeling for spectral element methods: current developments in {Nektar++} and further perspectives}, journal = {arXiv preprint arXiv:2201.05404}, year = {2022}, groups = {core}, doi = {10.48550/arXiv.2201.05404} }In this paper, we present recent efforts to develop reduced order modeling (ROM) capabilities for spectral element methods (SEM). Namely, we detail the implementation of ROM for both continuous Galerkin and discontinuous Galerkin methods in the spectral/hp element library Nektar++. The ROM approaches adopted are intrusive methods based on the proper orthogonal decomposition (POD). They admit an offline-online decomposition, such that fast evaluations for parameter studies and many-queries are possible. An affine parameter dependency is exploited such that the reduced order model can be evaluated independent of the large-scale discretization size. The implementation in the context of SEM can be found in the open-source model reduction software ITHACA-SEM.
2021
- Z.-G. Yan, Y. Pan, G. Castiglioni, K. Hillewaert, J. Peiró, D. Moxey and S. J. SherwinBiBTeX AbstractNektar++: Design and implementation of an implicit, spectral/hp element, compressible flow solver using a Jacobian-free Newton Krylov approachComputers & Mathematics with Applications, 81, pp. 351–372, 2021. doi 10.1016/j.camwa.2020.03.009
@article{2021:yan.pan.ea:nektar, author = {Yan, Zhen-Guo and Pan, Yu and Castiglioni, Giacomo and Hillewaert, Koen and Peir{\'o}, Joaquim and Moxey, David and Sherwin, Spencer J}, title = {Nektar++: Design and implementation of an implicit, spectral/hp element, compressible flow solver using a Jacobian-free Newton Krylov approach}, journal = {Computers \& Mathematics with Applications}, year = {2021}, volume = {81}, pages = {351--372}, publisher = {Elsevier}, groups = {core}, doi = {10.1016/j.camwa.2020.03.009} }At high Reynolds numbers the use of explicit in time compressible flow simulations with spectral/ element discretization can become significantly limited by time step. To alleviate this limitation we extend the capability of the spectral/ element open-source software framework, Nektar++, to include an implicit discontinuous Galerkin compressible flow solver. The integration in time is carried out by a singly diagonally implicit Runge-Kutta method. The non-linear system arising from the implicit time integration is iteratively solved by the Jacobian-free Newton Krylov (JFNK) method. A favorable feature of the JFNK approach is its extensive use of the explicit operators available from the previous explicit in time implementation. The functionalities of different building blocks of the implicit solver are analyzed from the point of view of software design and placed in appropriate hierarchical levels in the C++ libraries. In the detailed implementation, the contributions of different parts of the solver to computational cost, memory consumption and programming complexity are also analyzed. A combination of analytical and numerical methods is adopted to simplify the programming complexity in forming the preconditioning matrix. The solver is verified and tested using cases such as manufactured compressible Poiseuille flow, Taylor-Green vortex, turbulent flow over a circular cylinder at Re=3900 and shock wave boundary-layer interaction. The results show that the implicit solver can speed-up the simulations while maintaining good simulation accuracy.
2020
- D. Moxey, C. D. Cantwell, Y. Bao, A. Cassinelli, G. Castiglioni, S. Chun, E. Juda, E. Kazemi, K. Lackhove, J. Marcon, G. Mengaldo, D. Serson, M. Turner, H. Xu, J. Peiró, R. M. Kirby and S. J. SherwinBiBTeX Abstract\emphNektar++: enhancing the capability and application of high-fidelity spectral/hp element methodsComputer Physics Communications, 249, p. 107110, 2020. doi 10.1016/j.cpc.2019.107110
@article{2020:moxey.cantwell.ea:nektar, author = {Moxey, D. and Cantwell, C. D. and Bao, Y. and Cassinelli, A. and Castiglioni, G. and Chun, S. and Juda, E. and Kazemi, E. and Lackhove, K. and Marcon, J. and Mengaldo, G. and Serson, D. and Turner, M. and Xu, H. and Peir\'o, J. and Kirby, R. M. and Sherwin, S. J.}, title = {\emph{Nektar++}: enhancing the capability and application of high-fidelity spectral/$hp$ element methods}, journal = {Computer Physics Communications}, year = {2020}, volume = {249}, pages = {107110}, doi = {10.1016/j.cpc.2019.107110}, groups = {core} }\emphNektar++ is an open-source framework that provides a flexible, performant and scalable platform for the development of solvers for partial differential equations using the high-order spectral/hp element method. In particular, \emphNektar++ aims to overcome the complex implementation challenges that are often associated with high-order methods, thereby allowing them to be more readily used in a wide range of application areas. In this paper, we present the algorithmic, implementation and application developments associated with our \emphNektar++ version 5.0 release. We describe some of the key software and performance developments, including our strategies on parallel I/O, on \emphin situ processing, the use of collective operations for exploiting current and emerging hardware, and interfaces to enable multi-solver coupling. Furthermore, we provide details on a newly developed Python interface that enable more rapid on-boarding of new users unfamiliar with spectral/hp element methods, C++ and/or \emphNektar++. This release also incorporates a number of numerical method developments – in particular: the method of moving frames (MMF), which provides an additional approach for the simulation of equations on embedded curvilinear manifolds and domains; a means of handling spatially variable polynomial order; and a novel technique for quasi-3D simulations (which combine a 2D spectral element and 1D Fourier spectral method) to permit spatially-varying perturbations to the geometry in the homogeneous direction. Finally, we demonstrate the new application-level features provided in this release, namely: a facility for generating high-order curvilinear meshes called \emphNekMesh; a novel new \emphAcousticSolver for aeroacoustic problems; our development of a ‘thick’ strip model for the modelling of fluid-structure interaction (FSI) problems in the context of vortex-induced vibrations (VIV). We conclude by commenting on some lessons learned and by discussing some directions for future code development and expansion. - D. Moxey, R. Amici and R. M. KirbyBiBTeX AbstractEfficient matrix-free high-order finite element evaluation for simplicial elementsSIAM Journal on Scientific Computing, 42 (3), pp. C97–C123, 2020. doi 10.1137/19M1246523
@article{2020:moxey.amici.ea:efficient, author = {Moxey, D. and Amici, R. and Kirby, R. M.}, title = {Efficient matrix-free high-order finite element evaluation for simplicial elements}, journal = {SIAM Journal on Scientific Computing}, year = {2020}, volume = {42}, number = {3}, pages = {C97-C123}, groups = {core}, doi = {10.1137/19M1246523} }With the gap between processor clock speeds and memory bandwidth speeds continuing to increase, the use of arithmetically intense schemes, such as high-order finite element methods, continues to be of considerable interest. In particular, the use of matrix-free formulations of finite element operators for tensor-product elements of quadrilaterals in two dimensions and hexahedra in three dimensions, in combination with single-instruction multiple-data (SIMD) instruction sets, is a well-studied topic at present for the efficient implicit solution of elliptic equations. However, a considerable limiting factor for this approach is the use of meshes comprising of only quadrilaterals or hexahedra, the creation of which is still an open problem within the mesh generation community. In this article, we study the efficiency of high-order finite element operators for the Helmholtz equation with a focus on extending this approach to unstructured meshes of triangles, tetrahedra and prismatic elements using the spectral/hp element method and corresponding tensor-product bases for these element types. We show that although performance is naturally degraded when going from hexahedra to these simplicial elements, efficient implementations can still be obtained that are capable of attaining 50–70% of the peak FLOPS of processors with both AVX2 and AVX512 instruction sets. - J. Eichstädt, M. Vymazal, D. Moxey and J. PeiróBiBTeX AbstractA comparison of the shared-memory parallel programming models OpenMP, OpenACC and Kokkos in the context of implicit solvers for high-order FEMComputer Physics Communications, 255, p. 107245, 2020. doi 10.1016/j.cpc.2020.107245
@article{2020:eichstadt.vymazal.ea:comparison, author = {Eichst\"adt, J. and Vymazal, M. and Moxey, D. and Peir\'o, J.}, title = {A comparison of the shared-memory parallel programming models OpenMP, OpenACC and Kokkos in the context of implicit solvers for high-order FEM}, journal = {Computer Physics Communications}, year = {2020}, volume = {255}, pages = {107245}, groups = {core}, doi = {10.1016/j.cpc.2020.107245} }We consider the application of three performance-portable programming models in the context of a high-order spectral element, implicit time-stepping solver for the Navier-Stokes equations. We aim to evaluate whether the use of these models allows code developers to deliver high-performance solvers for computational fluid dynamics simulations that are capable of effectively utilising both many-core CPU and GPU architectures. Using the core elliptic solver for the Navier-Stokes equations as a benchmarking guide, we evaluate the performance of these models on a range of unstructured meshes and give guidelines for the translation of existing codebases and their data structures to these models.
2019
- M. Vymazal, D. Moxey, S. Sherwin, C. D. Cantwell and R. M. KirbyBiBTeX AbstractOn weak Dirichlet boundary conditions for elliptic problems in the continuous Galerkin methodJournal of Computational Physics, 394, pp. 732–744, 2019. doi 10.1016/j.jcp.2019.05.021
@article{2019:vymazal.moxey.ea:on, author = {Vymazal, M. and Moxey, D. and Sherwin, S. and Cantwell, C. D. and Kirby, R. M.}, title = {On weak {Dirichlet} boundary conditions for elliptic problems in the continuous {Galerkin} method}, journal = {Journal of Computational Physics}, year = {2019}, volume = {394}, pages = {732--744}, doi = {10.1016/j.jcp.2019.05.021}, groups = {core} }We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain - groups of elements that support a piecewise-polynomial continuous expansion. This step allows us to identify a new weak formulation of Dirichlet boundary condition in the continuous framework. We show that the boundary condition leads to a stable discretization with a single parameter insensitive to mesh size and polynomial order of the expansion. The robustness of the approach is demonstrated on several numerical examples. - J. Marcon, D. A. Kopriva, S. J. Sherwin and J. PeiróBiBTeX AbstractA high resolution PDE approach to quadrilateral mesh generationJournal of Computational Physics, 399, p. 108918, 2019. doi 10.1016/j.jcp.2019.108918
@article{2019:marcon.kopriva.ea:high, author = {Marcon, Julian and Kopriva, David A and Sherwin, Spencer J and Peir{\'o}, Joaquim}, title = {A high resolution {PDE} approach to quadrilateral mesh generation}, journal = {Journal of Computational Physics}, year = {2019}, volume = {399}, pages = {108918}, publisher = {Elsevier}, groups = {core}, doi = {10.1016/j.jcp.2019.108918} }We describe a high order technique to generate quadrilateral decompositions and meshes for complex two dimensional domains using spectral elements in a field guided procedure. Inspired by cross field methods, we never actually compute crosses. Instead, we compute a high order accurate guiding field using a continuous Galerkin (CG) or discontinuous Galerkin (DG) spectral element method to solve a Laplace equation for each of the field variables using the open source code Nektar++. The spectral method provides spectral convergence and sub-element resolution of the fields. The DG approximation allows meshing of corners that are not multiples of π/2 in a discretization consistent manner, when needed. The high order field can then be exploited to accurately find irregular nodes, and can be accurately integrated using a high order separatrix integration method to avoid features like limit cycles. The result is a mesh with naturally curved quadrilateral elements that do not need to be curved a posteriori to eliminate invalid elements. The mesh generation procedure is implemented in the open source mesh generation program NekMesh. - C. D. Cantwell and A. S. NielsenBiBTeX AbstractA minimally intrusive low-memory approach to resilience for existing transient solversJournal of Scientific Computing, 78, pp. 565–581, 2019. doi 10.1007/s10915-018-0778-7
@article{2019:cantwell.nielsen:minimally, author = {Cantwell, Chris D and Nielsen, Allan S}, title = {A minimally intrusive low-memory approach to resilience for existing transient solvers}, journal = {Journal of Scientific Computing}, year = {2019}, volume = {78}, pages = {565--581}, publisher = {Springer}, groups = {core}, doi = {10.1007/s10915-018-0778-7} }We propose a novel, minimally intrusive approach to adding fault tolerance to existing complex scientific simulation codes, used for addressing a broad range of time-dependent problems on the next generation of supercomputers. Exascale systems have the potential to allow much larger, more accurate and scale-resolving simulations of transient processes than can be performed on current petascale systems. However, with a much larger number of components, exascale computers are expected to suffer a node failure every few minutes. Many existing parallel simulation codes are not tolerant of these failures and existing resilience methodologies would necessitate major modifications or redesign of the application. Our approach combines the proposed user-level failure mitigation extensions to the Message-Passing Interface (MPI), with the concepts of message-logging and remote in-memory checkpointing, to demonstrate how to add scalable resilience to transient solvers. Logging MPI communication reduces the storage requirement of static data, such as finite element operators, and allows a spare MPI process to rebuild these data structures independently of other ranks. Remote in-memory checkpointing avoids disk I/O contention on large parallel filesystems. A prototype implementation is applied to Nektar++, a scalable, production-ready transient simulation framework. Forward-path and recovery-path performance of the resilience algorithm is analysed through experiments using the solver for the incompressible Navier-Stokes equations, and strong scaling of the approach is observed.
2018
- J. Yu, C. Yan and Z. JiangBiBTeX AbstractRevisit of dilation-based shock capturing for discontinuous Galerkin methodsApplied Mathematics and Mechanics, 39 (3), pp. 379–394, 2018. doi 10.1007/s10483-018-2302-7
@article{2018:yu.yan.ea:revisit, author = {Yu, Jian and Yan, Chao and Jiang, Zhenhua}, title = {Revisit of dilation-based shock capturing for discontinuous Galerkin methods}, journal = {Applied Mathematics and Mechanics}, year = {2018}, volume = {39}, number = {3}, pages = {379--394}, publisher = {Springer}, doi = {10.1007/s10483-018-2302-7}, groups = {core} }The idea of using velocity dilation for shock capturing is revisited in this paper, combined with the discontinuous Galerkin method. The value of artificial viscosity is determined using direct dilation instead of its higher order derivatives to reduce cost and degree of difficulty in computing derivatives. Alternative methods for estimating the element size of large aspect ratio and smooth artificial viscosity are proposed to further improve robustness and accuracy of the model. Several benchmark tests are conducted, ranging from subsonic to hypersonic flows involving strong shocks. Instead of adjusting empirical parameters to achieve optimum results for each case, all tests use a constant parameter for the model with reasonable success, indicating excellent robustness of the method. The model is only limited to third-order accuracy for smooth flows. This limitation may be relaxed by using a switch or a wall function. Overall, the model is a good candidate for compressible flows with potentials of further improvement. - G. Mengaldo, D. De Grazia, R. C. Moura and S. J. SherwinBiBTeX AbstractSpatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustnessJournal of Computational Physics, 2018. doi 10.1016/j.jcp.2017.12.019
@article{2018:mengaldo.de-grazia.ea:spatial, author = {Mengaldo, Gianmarco and De Grazia, Daniele and Moura, Rodrigo C and Sherwin, Spencer J}, title = {Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness}, journal = {Journal of Computational Physics}, year = {2018}, publisher = {Elsevier}, doi = {10.1016/j.jcp.2017.12.019}, groups = {core} }This study focuses on the dispersion and diffusion characteristics of high-order energy-stable flux reconstruction (ESFR) schemes via the spatial eigensolution analysis framework proposed in doi.org/10.1016/j.compfluid.2017.09.016. The analysis is performed for five ESFR schemes, where the parameter c dictating the properties of the specific scheme recovered is chosen such that it spans the entire class of ESFR methods, also referred to as VCJH schemes, proposed in doi.org/10.1007/s10915-010-9420-z. In particular, we used five values of c, two that correspond to its lower and upper bounds and the others that identify three schemes that are linked to common high-order methods, namely the ESFR recovering two versions of discontinuous Galerkin methods and one recovering the spectral difference scheme. The performance of each scheme is assessed when using different numerical intercell fluxes (e.g. different levels of upwinding), ranging from under- to over-upwinding. In contrast to the more common temporal analysis, the spatial eigensolution analysis framework adopted here allows one to grasp crucial insights into the diffusion and dispersion properties of FR schemes for problems involving non-periodic boundary conditions, typically found in open-flow problems, including turbulence, unsteady aerodynamics and aeroacoustics. - J. Cohen, J. Marcon, M. Turner, C. Cantwell, S. J. Sherwin, J. Peiró and D. MoxeyBiBTeX AbstractSimplifying high-order mesh generation for computational scientists2018. doi 10.5281/zenodo.3760858
@inproceedings{2018:cohen.marcon.ea:simplifying, author = {Cohen, Jeremy and Marcon, Julian and Turner, Michael and Cantwell, Chris and Sherwin, SJ and Peir{\'o}, Joaquim and Moxey, David}, title = {Simplifying high-order mesh generation for computational scientists}, year = {2018}, organization = {CEUR Workshop Proceedings}, groups = {core}, doi = {10.5281/zenodo.3760858} }Computational modelling is now tightly integrated into many fields of research in science and industry. Computa- tional fluid dynamics software, for example, gives engineers the ability to model fluid flow around complex geometries defined in Computer-Aided Design (CAD) packages, without the expense of constructing large wind tunnel experiments. However, such modelling requires translation from an initial CAD geometry to a mesh of many small elements that modelling software uses to represent the approximate solution in the numerical method. Generating sufficiently high-quality meshes for simulation is a time-consuming, iterative and error-prone process that is often complicated by the need to interact with multiple command-line tools to generate and visualise the mesh data. In this paper we describe our approach to overcoming this complexity through the addition of a meshing console to Nekkloud, a science gateway for simplifying access to the functionality of the Nektar++ spectral/hp element framework. The meshing console makes use of the NekMesh tool in Nektar++ to help reduce the complexity of the mesh generation process. It offers a web-based interface for specifying parameters, undertaking meshing and visualising results. The meshing console enables Nekkloud to offer support for a full, end-to-end simulation pipeline from initial CAD geometry to simulation results. - M. Bareford, N. Johnson and M. WeilandCray User Group Proceedings, Stockholm, Sweden, 2018.BiBTeX Abstract
@article{2018:bareford.johnson.ea:improving, author = {Bareford, Michael and Johnson, Nick and Weiland, Michele}, title = {Improving Nektar++ IO performance for cray XC architecture}, journal = {Cray User Group Proceedings, Stockholm, Sweden}, year = {2018}, groups = {core}, url = {https://cug.org/proceedings/cug2018_proceedings/includes/files/pap111s2-file1.pdf} }Future machine architectures are likely to have higher core counts placing tougher demands on the parallel IO routinely performed by codes such as Nektar++, an open- source MPI-based spectral element code that is widely used within the UK CFD community. There is a need therefore to compare the performance of different IO techniques on today’s platforms in order to determine the most promising candidates for exascale machines. We measure file access times for three IO methods, XML, HDF5 and SIONlib, over a range of core counts (up to 6144) on the ARCHER Cray XC-30. The first of these (XML) follows a file-per-process approach, whereas HDF5 and SIONlib allow one to manage a single shared file, thus minimising meta IO costs. We conclude that SIONlib is the preferred choice for single-shared file as a result of two advantages, lower decompositional overhead and a greater responsiveness to Lustre file customisations.
2017
- A. R. Winters, R. C. Moura, G. Mengaldo, G. J. Gassner, S. Walch, J. Peiro and S. J. SherwinBiBTeXA comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computationsarXiv preprint arXiv:1711.10180, 2017. doi 10.48550/arXiv.1711.10180
@article{2017:winters.moura.ea:comparative, author = {Winters, Andrew R and Moura, Rodrigo C and Mengaldo, Gianmarco and Gassner, Gregor J and Walch, Stefanie and Peiro, Joaquim and Sherwin, Spencer J}, title = {A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations}, journal = {arXiv preprint arXiv:1711.10180}, year = {2017}, doi = {10.48550/arXiv.1711.10180}, groups = {core} } - D. Moxey, C. D. Cantwell, G. Mengaldo, D. Serson, D. Ekelschot, J. Peiró, S. J. Sherwin and R. M. KirbyBiBTeXTowards p-adaptive spectral/hp element methods for modelling industrial flowsin Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, Springer, 2017, pp. 63–79. doi 10.1007/978-3-319-65870-4_4
@incollection{2017:moxey.cantwell.ea:towards, author = {Moxey, D and Cantwell, CD and Mengaldo, G and Serson, D and Ekelschot, D and Peir{\'o}, J and Sherwin, SJ and Kirby, RM}, title = {Towards p-adaptive spectral/hp element methods for modelling industrial flows}, booktitle = {Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016}, publisher = {Springer}, year = {2017}, pages = {63--79}, doi = {10.1007/978-3-319-65870-4_4}, groups = {core} } - R. C. Moura, G. Mengaldo, J. Peiró and S. J. SherwinBiBTeXAn LES setting for DG-based implicit LES with insights on dissipation and robustnessin Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, Springer, 2017, pp. 161–173. doi 10.1007/978-3-319-65870-4_10
@incollection{2017:moura.mengaldo.ea:setting, author = {Moura, Rodrigo C and Mengaldo, Gianmarco and Peir{\'o}, Joaquim and Sherwin, Spencer J}, title = {An LES setting for DG-based implicit LES with insights on dissipation and robustness}, booktitle = {Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016}, publisher = {Springer}, year = {2017}, pages = {161--173}, doi = {10.1007/978-3-319-65870-4_10}, groups = {core} } - R. C. Moura, G. Mengaldo, J. Peiró and S. J. SherwinBiBTeX AbstractOn the eddy-resolving capability of high-order discontinuous Galerkin approaches to implicit LES/under-resolved DNS of Euler turbulenceJournal of Computational Physics, 330, pp. 615–623, 2017. doi 10.1016/j.compfluid.2017.09.016
@article{2017:moura.mengaldo.ea:on, author = {Moura, R.C. and Mengaldo, G. and Peir{\'o}, J. and Sherwin, S.J.}, title = {On the eddy-resolving capability of high-order discontinuous {Galerkin} approaches to implicit {LES}/under-resolved {DNS} of {Euler} turbulence}, journal = {Journal of Computational Physics}, year = {2017}, volume = {330}, pages = {615--623}, publisher = {Elsevier}, groups = {core}, doi = {10.1016/j.compfluid.2017.09.016} }The study focusses on the dispersion and diffusion characteristics of discontinuous spectral element methods - specifically discontinuous Galerkin (DG) - via the spatial eigensolution analysis framework built around a one-dimensional linear problem, namely the linear advection equation. Dispersion and diffusion characteristics are of critical importance when dealing with under-resolved computations, as they affect both the numerical stability of the simulation and the solution accuracy. The spatial eigensolution analysis carried out in this paper complements previous analyses based on the temporal approach, which are more commonly found in the literature. While the latter assumes periodic boundary conditions, the spatial approach assumes inflow/outflow type boundary conditions and is therefore better suited for the investigation of open flows typical of aerodynamic problems, including transitional and fully turbulent flows and aeroacoustics. The influence of spurious/reflected eigenmodes is assessed with regard to the presence of upwind dissipation, naturally present in DG methods. This provides insights into the accuracy and robustness of these schemes for under-resolved computations, including under-resolved direct numerical simulation (uDNS) and implicit large-eddy simulation (iLES). The results estimated from the spatial eigensolution analysis are verified using the one-dimensional linear advection equation and successively by performing two-dimensional compressible Euler simulations that mimic (spatially developing) grid turbulence. - G. Mengaldo, R. C. Moura, B. Giralda, J. Peiró and S. J. SherwinBiBTeX AbstractSpatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit LESComputers & Fluids, 2017. doi 10.1016/j.compfluid.2017.09.016
@article{2017:mengaldo.moura.ea:spatial, author = {Mengaldo, G. and Moura, R.C. and Giralda, B. and Peir{\'o}, J. and Sherwin, S.J.}, title = {Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit {LES}}, journal = {Computers \& Fluids}, year = {2017}, publisher = {Elsevier}, groups = {core}, doi = {10.1016/j.compfluid.2017.09.016} }The study focusses on the dispersion and diffusion characteristics of discontinuous spectral element methods - specifically discontinuous Galerkin (DG) - via the spatial eigensolution analysis framework built around a one-dimensional linear problem, namely the linear advection equation. Dispersion and diffusion characteristics are of critical importance when dealing with under-resolved computations, as they affect both the numerical stability of the simulation and the solution accuracy. The spatial eigensolution analysis carried out in this paper complements previous analyses based on the temporal approach, which are more commonly found in the literature. While the latter assumes periodic boundary conditions, the spatial approach assumes inflow/outflow type boundary conditions and is therefore better suited for the investigation of open flows typical of aerodynamic problems, including transitional and fully turbulent flows and aeroacoustics. The influence of spurious/reflected eigenmodes is assessed with regard to the presence of upwind dissipation, naturally present in DG methods. This provides insights into the accuracy and robustness of these schemes for under-resolved computations, including under-resolved direct numerical simulation (uDNS) and implicit large-eddy simulation (iLES). The results estimated from the spatial eigensolution analysis are verified using the one-dimensional linear advection equation and successively by performing two-dimensional compressible Euler simulations that mimic (spatially developing) grid turbulence.
2016
- S. Yakovlev, D. Moxey, R. M. Kirby and S. J. SherwinBiBTeX AbstractTo CG or to HDG: A Comparative Study in 3DJournal of Scientific Computing, 67, pp. 192–220, 2016. doi 10.1007/s10915-015-0076-6
@article{2016:yakovlev.moxey.ea:to, author = {Yakovlev, S. and Moxey, D. and Kirby, R. M. and Sherwin, S. J.}, title = {To CG or to HDG: A Comparative Study in 3D}, journal = {Journal of Scientific Computing}, year = {2016}, volume = {67}, pages = {192--220}, month = jul, doi = {10.1007/s10915-015-0076-6}, issn = {0885-7474}, day = {28}, publicationstatus = {accepted}, groups = {core} }Since the inception of discontinuous Galerkin (DG) methods for elliptic problems, there has existed a question of whether DG methods can be made more computationally efficient than continuous Galerkin (CG) methods. Fewer degrees of freedom, approximation properties for elliptic problems together with the number of optimization techniques, such as static condensation, available within CG framework made it challenging for DG methods to be competitive until recently. However, with the introduction of a static-condensation-amenable DG method the hybridizable discontinuous Galerkin (HDG) method it has become possible to perform a realistic comparison of CG and HDG methods when applied to elliptic problems. In this work, we extend upon an earlier 2D comparative study, providing numerical results and discussion of the CG and HDG method performance in three dimensions. The comparison categories covered include steady-state elliptic and time-dependent parabolic problems, various element types and serial and parallel performance. The postprocessing technique, which allows for superconvergence in the HDG case, is also discussed. Depending on the direct linear system solver used and the type of the problem (steady-state vs. time-dependent) in question the HDG method either outperforms or demonstrates a comparable performance when compared with the CG method. The HDG method however falls behind performance-wise when the iterative solver is used, which indicates the need for an effective preconditioning strategy for the method. - D. Serson, J. R. Meneghini and S. J. SherwinBiBTeX AbstractVelocity-correction schemes for the incompressible Navier-Stokes equations in general coordinate systemsJournal of Computational Physics, 316, pp. 243–254, 2016. doi 10.1016/j.jcp.2016.04.026
@article{2016:serson.meneghini.ea:velocity-correction, author = {Serson, D and Meneghini, JR and Sherwin, SJ}, title = {Velocity-correction schemes for the incompressible Navier-Stokes equations in general coordinate systems}, journal = {Journal of Computational Physics}, year = {2016}, volume = {316}, pages = {243--254}, month = jul, doi = {10.1016/j.jcp.2016.04.026}, issn = {0021-9991}, eissn = {1090-2716}, day = {1}, publicationstatus = {published}, groups = {core} }This paper presents methods of including coordinate transformations into the solution of the incompressible Navier-Stokes equations using the velocity-correction scheme, which is commonly used in the numerical solution of unsteady incompressible flows. This is important when the transformation leads to symmetries that allow the use of more efficient numerical techniques, like employing a Fourier expansion to discretize a homogeneous direction. Two different approaches are presented: in the first approach all the influence of the mapping is treated explicitly, while in the second the mapping terms related to convection are treated explicitly, with the pressure and viscous terms treated implicitly. Through numerical results, we demonstrate how these methods maintain the accuracy of the underlying high-order method, and further apply the discretisation strategy to problems where mixed Fourier-spectral/hp element discretisations can be applied, thereby extending the usefulness of this discretisation technique. - J. Peiro, D. Moxey, S. J. Sherwin and D. EkelschotComputers and Structures, 2016.BiBTeX
@article{2016:peiro.moxey.ea:p-adaptation, author = {Peiro, J and Moxey, D and Sherwin, S.J. and Ekelschot, D.}, title = {A p-adaptation method for compressible flow problems using a goal-based error indicator}, journal = {Computers and Structures}, year = {2016}, url = {http://hdl.handle.net/10044/1/30414}, groups = {core} } - R. C. Moura, S. J. Sherwin and J. PeiroBiBTeX AbstractEigensolution analysis of spectral/hp continuous Galerkin approximations to advection-diffusion problems: Insights into spectral vanishing viscosityJournal of Computational Physics, 307, pp. 401–422, 2016. doi 10.1016/j.jcp.2015.12.009
@article{2016:moura.sherwin.ea:eigensolution, author = {Moura, R. C. and Sherwin, S. J. and Peiro, J}, title = {Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection-diffusion problems: Insights into spectral vanishing viscosity}, journal = {Journal of Computational Physics}, year = {2016}, volume = {307}, pages = {401--422}, month = feb, doi = {10.1016/j.jcp.2015.12.009}, issn = {0021-9991}, eissn = {1090-2716}, day = {15}, publicationstatus = {accepted}, groups = {core} }This study addresses linear dispersion-diffusion analysis for the spectral/hp continuous Galerkin (CG) formulation in one dimension. First, numerical dispersion and diffusion curves are obtained for the advection-diffusion problem and the role of multiple eigencurves peculiar to spectral/hp methods is discussed. From the eigencurves’ behaviour, we observe that CG might feature potentially undesirable non-smooth dispersion/diffusion characteristics for under-resolved simulations of problems strongly dominated by either convection or diffusion. Subsequently, the linear advection equation augmented with spectral vanishing viscosity (SVV) is analysed. Dispersion and diffusion characteristics of CG with SVV-based stabilization are verified to display similar non-smooth features in flow regions where convection is much stronger than dissipation or vice-versa, owing to a dependency of the standard SVV operator on a local Peclet number. First a modification is proposed to the traditional SVV scaling that enforces a globally constant Peclet number so as to avoid the previous issues. In addition, a new SVV kernel function is suggested and shown to provide a more regular behaviour for the eigencurves along with a consistent increase in resolution power for higher-order discretizations, as measured by the extent of the wavenumber range where numerical errors are negligible. The dissipation characteristics of CG with the SVV modifications suggested are then verified to be broadly equivalent to those obtained through upwinding in the discontinuous Galerkin (DG) scheme. Nevertheless, for the kernel function proposed, the full upwind DG scheme is found to have a slightly higher resolution power for the same dissipation levels. These results show that improved CG-SVV characteristics can be pursued via different kernel functions with the aid of optimization algorithms. - G. Mengaldo, D. de Grazia, P. E. Vincent and S. J. SherwinBiBTeX AbstractOn the Connections Between Discontinuous Galerkin and Flux Reconstruction Schemes: Extension to Curvilinear MeshesJournal of Scientific Computing, 67, pp. 1272–1292, 2016. doi 10.1007/s10915-015-0119-z
@article{2016:mengaldo.grazia.ea:on, author = {Mengaldo, G. and de Grazia, D. and Vincent, P. E. and Sherwin, S. J.}, title = {On the Connections Between Discontinuous Galerkin and Flux Reconstruction Schemes: Extension to Curvilinear Meshes}, journal = {Journal of Scientific Computing}, year = {2016}, volume = {67}, pages = {1272--1292}, month = oct, doi = {10.1007/s10915-015-0119-z}, issn = {0885-7474}, day = {19}, publicationstatus = {accepted}, groups = {core} }This paper investigates the connections between many popular variants of the well-established discontinuous Galerkin method and the recently developed high-order flux reconstruction approach on irregular tensor-product grids. We explore these connections by analysing three nodal versions of tensor-product discontinuous Galerkin spectral element approximations and three types of flux reconstruction schemes for solving systems of conservation laws on irregular tensor-product meshes. We demonstrate that the existing connections established on regular grids are also valid on deformed and curved meshes for both linear and nonlinear problems, provided that the metric terms are accounted for appropriately. We also find that the aliasing issues arising from nonlinearities either due to a deformed/curved elements or due to the nonlinearity of the equations are equivalent and can be addressed using the same strategies both in the discontinuous Galerkin method and in the flux reconstruction approach. In particular, we show that the discontinuous Galerkin and the flux reconstruction approach are equivalent also when using higher-order quadrature rules that are commonly employed in the context of over- or consistent-integration-based dealiasing methods. The connections found in this work help to complete the picture regarding the relations between these two numerical approaches and show the possibility of using over- or consistent-integration in an equivalent manner for both the approaches. - A. Bolis, C. D. Cantwell, D. Moxey, D. Serson and S. J. SherwinBiBTeXAn adaptable parallel algorithm for the direct numerical simulation of incompressible turbulent flows using a Fourier spectral/hp element method and MPI virtual topologiesComputer Physics Communications, 2016. doi 10.1016/j.cpc.2016.04.011
@article{2016:bolis.cantwell.ea:adaptable, author = {Bolis, A and Cantwell, CD and Moxey, D and Serson, D and Sherwin, SJ}, title = {An adaptable parallel algorithm for the direct numerical simulation of incompressible turbulent flows using a Fourier spectral/hp element method and MPI virtual topologies}, journal = {Computer Physics Communications}, year = {2016}, month = apr, doi = {10.1016/j.cpc.2016.04.011}, issn = {0010-4655}, publicationstatus = {published}, groups = {core} } - Y. Bao, R. Palacios, J. M. R. Graham and S. J. SherwinJournal of Computational Physics, 2016.BiBTeX
@article{2016:bao.palacios.ea:generalized, author = {Bao, Y and Palacios, R and Graham, JMR and Sherwin, SJ}, title = {Generalized thick strip modelling for vortex-induced vibration of long flexible cylinders}, journal = {Journal of Computational Physics}, year = {2016}, url = {http://hdl.handle.net/10044/1/33432}, groups = {core} }
2015
- D. Moxey, M. Hazan, S. J. Sherwin and J. PeiroBiBTeX AbstractCurvilinear mesh generation for boundary layer problemsNotes on Numerical Fluid Mechanics and Multidisciplinary Design, 128, pp. 41–64, 2015. doi 10.1007/978-3-319-12886-3_3
@article{2015:moxey.hazan.ea:curvilinear, author = {Moxey, D. and Hazan, M. and Sherwin, S. J. and Peiro, J.}, title = {Curvilinear mesh generation for boundary layer problems}, journal = {Notes on Numerical Fluid Mechanics and Multidisciplinary Design}, year = {2015}, volume = {128}, pages = {41--64}, month = jan, doi = {10.1007/978-3-319-12886-3_3}, issn = {1612-2909}, day = {1}, publicationstatus = {published}, groups = {core} }In this article, we give an overview of a new technique for unstructured curvilinear boundary layer grid generation, which uses the isoparametric mappings that define elements in an existing coarse prismatic grid to produce a refined mesh capable of resolving arbitrarily thin boundary layers. We demonstrate that the technique always produces valid grids given an initially valid coarse mesh, and additionally show how this can be extended to convert hybrid meshes to meshes containing only simplicial elements. - D. Moxey, M. D. Green, S. J. Sherwin and J. PeiroBiBTeXAn isoparametric approach to high-order curvilinear boundary-layer meshingCOMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 283, pp. 636–650, 2015. doi 10.1016/j.cma.2014.09.019
@article{2015:moxey.green.ea:isoparametric, author = {Moxey, D. and Green, M. D. and Sherwin, S. J. and Peiro, J.}, title = {An isoparametric approach to high-order curvilinear boundary-layer meshing}, journal = {COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING}, year = {2015}, volume = {283}, pages = {636--650}, month = jan, publisher = {ELSEVIER SCIENCE SA}, doi = {10.1016/j.cma.2014.09.019}, issn = {0045-7825}, keyword = {GRIDS}, language = {English}, day = {1}, publicationstatus = {published}, groups = {core} } - G. Mengaldo, G. D. De, D. Moxey, P. E. Vincent and S. J. SherwinBiBTeXDealiasing techniques for high-order spectral element methods on regular and irregular gridsJOURNAL OF COMPUTATIONAL PHYSICS, 299, pp. 56–81, 2015. doi 10.1016/j.jcp.2015.06.032
@article{2015:mengaldo.de.ea:dealiasing, author = {Mengaldo, G and De, Grazia D and Moxey, D and Vincent, PE and Sherwin, SJ}, title = {Dealiasing techniques for high-order spectral element methods on regular and irregular grids}, journal = {JOURNAL OF COMPUTATIONAL PHYSICS}, year = {2015}, volume = {299}, pages = {56--81}, doi = {10.1016/j.jcp.2015.06.032}, groups = {core} } - C. D. Cantwell, D. Moxey, A. Comerford, A. Bolis, G. Rocco, G. Mengaldo, D. De Grazia, S. Yakovlev, J.-E. Lombard, D. Ekelschot, B. Jordi, H. Xu, Y. Mohamied, C. Eskilsson, B. Nelson, P. Vos, C. Biotto, R. M. Kirby and S. J. SherwinBiBTeXNektar plus plus : An open-source spectral/hp element frameworkCOMPUTER PHYSICS COMMUNICATIONS, 192, pp. 205–219, 2015. doi 10.1016/j.cpc.2015.02.008
@article{2015:cantwell.moxey.ea:nektar, author = {Cantwell, C. D. and Moxey, D. and Comerford, A. and Bolis, A. and Rocco, G. and Mengaldo, G. and De Grazia, D. and Yakovlev, S. and Lombard, J-E. and Ekelschot, D. and Jordi, B. and Xu, H. and Mohamied, Y. and Eskilsson, C. and Nelson, B. and Vos, P. and Biotto, C. and Kirby, R. M. and Sherwin, S. J.}, title = {Nektar plus plus : An open-source spectral/hp element framework}, journal = {COMPUTER PHYSICS COMMUNICATIONS}, year = {2015}, volume = {192}, pages = {205--219}, month = jul, publisher = {ELSEVIER SCIENCE BV}, doi = {10.1016/j.cpc.2015.02.008}, issn = {0010-4655}, keyword = {SYSTEM}, language = {English}, day = {1}, publicationstatus = {published}, groups = {core} }
2014
- D. Moxey, D. Ekelschot, U. Keskin, S. J. Sherwin and J. PeiroBiBTeXA thermo-elastic analogy for high-order curvilinear meshing with control of mesh validity and qualityin 23RD INTERNATIONAL MESHING ROUNDTABLE (IMR23), 2014, 82, pp. 127–135. doi 10.1016/j.proeng.2014.10.378
@inproceedings{2014:moxey.ekelschot.ea:thermo-elastic, author = {Moxey, D. and Ekelschot, D. and Keskin, U. and Sherwin, S. J. and Peiro, J.}, title = {A thermo-elastic analogy for high-order curvilinear meshing with control of mesh validity and quality}, editor = {Persson, P. O. and Staten, M. L.}, booktitle = {23RD INTERNATIONAL MESHING ROUNDTABLE (IMR23)}, year = {2014}, series = {Procedia Engineering}, volume = {82}, pages = {127--135}, month = jan, organization = {London, ENGLAND}, publisher = {ELSEVIER SCIENCE BV}, doi = {10.1016/j.proeng.2014.10.378}, startyear = {2014}, startmonth = {Oct}, startday = {12}, finishyear = {2014}, finishmonth = {Oct}, finishday = {15}, issn = {1877-7058}, keyword = {Engineering}, language = {English}, conference = {23rd International Meshing Roundtable (IMR)}, day = {1}, publicationstatus = {published}, groups = {core} } - G. Mengaldo, D. De Grazia, J. Peiro, A. Farrington, F. Witherden, P. E. Vincent and S. J. SherwinBiBTeX AbstractA guide to the implementation of boundary conditions in compact high-order methods for compressible aerodynamicsin AIAA AVIATION 2014 -7th AIAA Theoretical Fluid Mechanics Conference, 2014. doi 10.2514/6.2014-2923
@inproceedings{2014:mengaldo.de-grazia.ea:guide, author = {Mengaldo, G. and De Grazia, D. and Peiro, J. and Farrington, A. and Witherden, F. and Vincent, P. E. and Sherwin, S. J.}, title = {A guide to the implementation of boundary conditions in compact high-order methods for compressible aerodynamics}, booktitle = {AIAA AVIATION 2014 -7th AIAA Theoretical Fluid Mechanics Conference}, year = {2014}, month = jan, doi = {10.2514/6.2014-2923}, isbn = {9781624102936}, day = {1}, publicationstatus = {published}, groups = {core} }The nature of boundary conditions, and how they are implemented, can have a significant impact on the stability and accuracy of a Computational Fluid Dynamics (CFD) solver. The objective of this paper is to assess how different boundary conditions impact the performance of compact discontinuous high-order spectral element methods (such as the discontinuous Galerkin method and the Flux Reconstruction approach), when these schemes are used to solve the Euler and compressible Navier-Stokes equations on unstructured grids. Specifically, the paper will investigate inflow/outflow and wall boundary conditions. In all studies the boundary conditions were enforced by modifying the boundary flux. For Riemann invariant (characteristic), slip and no-slip conditions we have considered a direct and an indirect enforcement of the boundary conditions, the first obtained by calculating the flux using the known solution at the given boundary while the second achieved by using a ghost state and by solving a Riemann problem. All computations were performed using the open-source software Nektar++ (www.nektar.info). - B. E. Jordi, C. J. Cotter and S. J. SherwinBiBTeXEncapsulated formulation of the selective frequency damping methodPHYSICS OF FLUIDS, 26 (3), 2014. doi 10.1063/1.4867482
@article{2014:jordi.cotter.ea:encapsulated, author = {Jordi, B. E. and Cotter, C. J. and Sherwin, S. J.}, title = {Encapsulated formulation of the selective frequency damping method}, journal = {PHYSICS OF FLUIDS}, year = {2014}, volume = {26}, number = {ARTN 034101}, month = mar, publisher = {AMER INST PHYSICS}, doi = {10.1063/1.4867482}, issn = {1070-6631}, issue = {3}, keyword = {WAKE}, language = {English}, day = {1}, publicationstatus = {published}, groups = {core} } - D. De Grazia, G. Mengaldo, D. Moxey, P. E. Vincent and S. J. SherwinBiBTeXConnections between the discontinuous Galerkin method and high-order flux reconstruction schemesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 75 (12), pp. 860–877, 2014. doi 10.1002/fld.3915
@article{2014:de-grazia.mengaldo.ea:connections, author = {De Grazia, D. and Mengaldo, G. and Moxey, D. and Vincent, P. E. and Sherwin, S. J.}, title = {Connections between the discontinuous Galerkin method and high-order flux reconstruction schemes}, journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS}, year = {2014}, volume = {75}, pages = {860--877}, month = aug, publisher = {WILEY-BLACKWELL}, doi = {10.1002/fld.3915}, issn = {0271-2091}, issue = {12}, keyword = {SPECTRAL DIFFERENCE METHOD}, language = {English}, day = {30}, publicationstatus = {published}, groups = {core} } - C. D. Cantwell, S. Yakovlev, R. M. Kirby, N. S. Peters and S. J. SherwinBiBTeXHigh-order spectral/hp element discretisation for reaction-diffusion problems on surfaces: Application to cardiac electrophysiologyJOURNAL OF COMPUTATIONAL PHYSICS, 257, pp. 813–829, 2014. doi 10.1016/j.jcp.2013.10.019
@article{2014:cantwell.yakovlev.ea:high-order, author = {Cantwell, C. D. and Yakovlev, S. and Kirby, R. M. and Peters, N. S. and Sherwin, S. J.}, title = {High-order spectral/hp element discretisation for reaction-diffusion problems on surfaces: Application to cardiac electrophysiology}, journal = {JOURNAL OF COMPUTATIONAL PHYSICS}, year = {2014}, volume = {257}, pages = {813--829}, month = jan, publisher = {ACADEMIC PRESS INC ELSEVIER SCIENCE}, doi = {10.1016/j.jcp.2013.10.019}, issn = {0021-9991}, keyword = {MESHES}, language = {English}, day = {15}, publicationstatus = {published}, groups = {core} } - A. Bolis, C. D. Cantwell, R. M. Kirby and S. J. SherwinBiBTeXFrom h to p efficiently: optimal implementation strategies for explicit time-dependent problems using the spectral/hp element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 75 (8), pp. 591–607, 2014. doi 10.1002/fld.3909
@article{2014:bolis.cantwell.ea:from, author = {Bolis, A. and Cantwell, C. D. and Kirby, R. M. and Sherwin, S. J.}, title = {From h to p efficiently: optimal implementation strategies for explicit time-dependent problems using the spectral/hp element method}, journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS}, year = {2014}, volume = {75}, pages = {591--607}, month = jul, publisher = {WILEY-BLACKWELL}, doi = {10.1002/fld.3909}, issn = {0271-2091}, issue = {8}, keyword = {STABILITY}, language = {English}, day = {20}, publicationstatus = {published}, groups = {core} }
2012
- R. M. Kirby, B. Cockburn and S. J. SherwinBiBTeX AbstractTo CG or to HDG: A Comparative StudyJournal of Scientific Computing, 51 (1), pp. 183–212, 2012. doi 10.1007/s10915-011-9501-7
@article{2012:kirby.cockburn.ea:to, author = {Kirby, Robert M. and Cockburn, Bernardo and Sherwin, Spencer J.}, title = {To CG or to HDG: A Comparative Study}, journal = {Journal of Scientific Computing}, year = {2012}, volume = {51}, pages = {183--212}, issue = {1}, doi = {10.1007/s10915-011-9501-7}, groups = {core} }Hybridization through the border of the elements (hybrid unknowns) combined with a Schur complement procedure (often called static condensation in the context of continuous Galerkin linear elasticity computations) has in various forms been advocated in the mathematical and engineering literature as a means of accomplishing domain decomposition, of obtaining increased accuracy and convergence results, and of algorithm optimization. Recent work on the hybridization of mixed methods, and in particular of the discontinuous Galerkin (DG) method, holds the promise of capitalizing on the three aforementioned properties; in particular, of generating a numerical scheme that is discontinuous in both the primary and flux variables, is locally conservative, and is computationally competitive with traditional continuous Galerkin (CG) approaches. In this paper we present both implementation and optimization strategies for the Hybridizable Discontinuous Galerkin (HDG) method applied to two dimensional elliptic operators. We implement our HDG approach within a spectral/hp element framework so that comparisons can be done between HDG and the traditional CG approach. We demonstrate that the HDG approach generates a global trace space system for the unknown that although larger in rank than the traditional static condensation system in CG, has significantly smaller bandwidth at moderate polynomial orders. We show that if one ignores set-up costs, above approximately fourth-degree polynomial expansions on triangles and quadrilaterals the HDG method can be made to be as efficient as the CG approach, making it competitive for time-dependent problems even before taking into consideration other properties of DG schemes such as their superconvergence properties and their ability to handle hp-adaptivity.
2011
- P. E. J. Vos, C. Eskilsson, A. Bolis, S. Chun, R. M. Kirby and S. J. SherwinBiBTeX AbstractA Generic Framework for Time-Stepping PDEs: General Linear Methods, Object-Oriented Implementations and Applications to Fluid ProblemsInternational Journal of Computational Fluid Dynamics, 25 (3), pp. 107–125, 2011. doi 10.1080/10618562.2011.575368
@article{2011:vos.eskilsson.ea:generic, author = {Vos, Peter E. J. and Eskilsson, Claes and Bolis, Alessandro and Chun, Sehun and Kirby, Robert M. and Sherwin, Spencer J.}, title = {A Generic Framework for Time-Stepping PDEs: General Linear Methods, Object-Oriented Implementations and Applications to Fluid Problems}, journal = {International Journal of Computational Fluid Dynamics}, year = {2011}, volume = {25}, pages = {107--125}, issue = {3}, doi = {10.1080/10618562.2011.575368}, groups = {core} }Time-stepping algorithms and their implementations are a critical component within the solution of time-dependent partial differential equations (PDEs). In this article, we present a generic framework,both in terms of algorithms and implementations, that allows an almost seamless switch between various explicit, implicit and implicit explicit (IMEX) time-stepping methods. We put particular emphasis on how to incorporate time-dependent boundary conditions, an issue that goes beyond classical ODE theory but which plays an important role in the time-stepping of the PDEs arising in computational fluid dynamics. Our algorithm is based upon J.C. Butcher’s unifying concept of general linear methods that we have extended to accommodate the family of IMEX schemes that are often used in engineering practice. In the article, we discuss design considerations and present an object-oriented implementation. Finally, we illustrate the use of the framework by applications to a model problem as well as to more complex fluid problems. - C. D. Cantwell, S. J. Sherwin, R. M. Kirby and P. H. J. KellyBiBTeX AbstractFrom h to p efficiently: Strategy selection for operator evaluation on hexahedral and tetrahedral elementsCOMPUTERS & FLUIDS, 43 (1), pp. 23–28, 2011. doi 10.1016/j.compfluid.2010.08.012
@article{2011:cantwell.sherwin.ea:from*1, author = {Cantwell, C. D. and Sherwin, S. J. and Kirby, R. M. and Kelly, P. H. J.}, title = {From h to p efficiently: Strategy selection for operator evaluation on hexahedral and tetrahedral elements}, journal = {COMPUTERS \& FLUIDS}, year = {2011}, volume = {43}, pages = {23--28}, month = apr, organization = {Lausanne, SWITZERLAND}, publisher = {PERGAMON-ELSEVIER SCIENCE LTD}, doi = {10.1016/j.compfluid.2010.08.012}, startyear = {2010}, startmonth = {Feb}, startday = {15}, finishyear = {2010}, finishmonth = {Feb}, finishday = {16}, issn = {0045-7930}, issue = {1}, keyword = {FLOW}, language = {English}, conference = {Symposium on High Accuracy Flow Simulations}, day = {1}, publicationstatus = {published}, groups = {core} }A spectral/hp element discretisation permits both geometric flexibility and beneficial convergence properties to be attained simultaneously. The choice of elemental polynomial order has a profound effect on the efficiency of different implementation strategies with their performance varying substantially for low and high order spectral/hp discretisations. We examine how careful selection of the strategy minimises computational cost across a range of polynomial orders in three dimensions and compare how different operators, and the choice of element shape, lead to different break-even points between the implementations. In three dimensions, higher expansion orders quickly lead to a large increase in the number of element-interior modes, particularly in hexahedral elements. For a typical boundary interior modal decomposition, this can rapidly lead to a poor performance from a global approach, while a sum-factorisation technique, exploiting the tensor-product structure of elemental expansions, leads to better performance. Furthermore, increased memory requirements may cause an implementation to show poor runtime performance on a given system, even if the strict operation count is minimal, due to detrimental caching effects and other machine-dependent factors. - C. D. Cantwell, S. J. Sherwin, R. M. Kirby and P. H. J. KellyBiBTeX AbstractFrom h to p Efficiently: Selecting the Optimal Spectral/hp Discretisation in Three DimensionsMATHEMATICAL MODELLING OF NATURAL PHENOMENA, 6 (3), pp. 84–96, 2011. doi 10.1051/mmnp/20116304
@article{2011:cantwell.sherwin.ea:from, author = {Cantwell, C. D. and Sherwin, S. J. and Kirby, R. M. and Kelly, P. H. J.}, title = {From h to p Efficiently: Selecting the Optimal Spectral/hp Discretisation in Three Dimensions}, journal = {MATHEMATICAL MODELLING OF NATURAL PHENOMENA}, year = {2011}, volume = {6}, pages = {84--96}, month = jan, publisher = {EDP SCIENCES S A}, doi = {10.1051/mmnp/20116304}, issn = {0973-5348}, issue = {3}, keyword = {FLOW}, language = {English}, day = {1}, publicationstatus = {published}, groups = {core} }There is a growing interest in high-order finite and spectral/hp element methods using continuous and discontinuous Galerkin formulations. In this paper we investigate the effect of h- and p-type refinement on the relationship between runtime performance and solution accuracy. The broad spectrum of possible domain discretisations makes establishing a performance-optimal selection non-trivial. Through comparing the runtime of different implementations for evaluating operators over the space of discretisations with a desired solution tolerance, we demonstrate how the optimal discretisation and operator implementation may be selected for a specified problem. Furthermore, this demonstrates the need for codes to support both low- and high-order discretisations.
2010
- P. E. J. Vos, S. J. Sherwin and R. M. KirbyBiBTeX AbstractFrom h to p efficiently: Implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisationsJOURNAL OF COMPUTATIONAL PHYSICS, 229 (13), pp. 5161–5181, 2010. doi 10.1016/j.jcp.2010.03.031
@article{2010:vos.sherwin.ea:from, author = {Vos, P. E. J. and Sherwin, S. J. and Kirby, R. M.}, title = {From h to p efficiently: Implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisations}, journal = {JOURNAL OF COMPUTATIONAL PHYSICS}, year = {2010}, volume = {229}, pages = {5161--5181}, month = jul, publisher = {ACADEMIC PRESS INC ELSEVIER SCIENCE}, doi = {10.1016/j.jcp.2010.03.031}, issn = {0021-9991}, issue = {13}, keyword = {STABLE PENALTY METHOD}, language = {English}, day = {1}, publicationstatus = {published}, groups = {core} }The spectral/hp element method can be considered as bridging the gap between the traditionally low order finite element method on one side and spectral methods on the other side. Consequently, a major challenge which arises in implementing the spectral/hp element methods is to design algorithms that perform efficiently for both low- and high-order spectral/hp discretisations, as well as discretisations in the intermediate regime. In this paper, we explain how the judicious use of different implementation strategies can be employed to achieve high efficiency across a wide range of polynomial orders. Furthermore, based upon this efficient implementation, we analyse which spectral/hp discretisation (which specific combination of mesh-size h and polynomial order P) minimises the computational cost to solve an elliptic problem up to a predefined level of accuracy. We investigate this question for a set of both smooth and non-smooth problems.
2008
- D. Barkley, H. M. Blackburn and S. J. SherwinBiBTeX AbstractDirect optimal growth analysis for timesteppersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 57 (9), pp. 1435–1458, 2008. doi 10.1002/fld.1824
@article{2008:barkley.blackburn.ea:direct, author = {Barkley, D. and Blackburn, H. M. and Sherwin, S. J.}, title = {Direct optimal growth analysis for timesteppers}, journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS}, year = {2008}, volume = {57}, pages = {1435--1458}, month = jul, organization = {Santa Fe, NM}, publisher = {JOHN WILEY \& SONS LTD}, doi = {10.1002/fld.1824}, startyear = {2007}, startmonth = {Mar}, startday = {24}, finishyear = {2007}, finishmonth = {Mar}, finishday = {28}, issn = {0271-2091}, issue = {9}, keyword = {MODES}, language = {English}, conference = {14th International Conference on Finite Elements in Flow Problems}, day = {30}, publicationstatus = {published}, groups = {core} }Methods are described for transient growth analysis of flows with arbitrary geometric complexity, where in particular the flow is not required to vary slowly in the streamwise direction. Emphasis is on capturing the global effects arising from localized convective stability in streamwise varying flows. The methods employ the timestepper’s approach in which a nonlinear Navier Stokes code is modified to provide evolution operators for both the forward and adjoint linearized equations. First, the underlying mathematical treatment in primitive flow variables is presented. Then, details are given for the inner level code modifications and outer level eigenvalue and SVD algorithms in the timestepper’s approach. Finally, some examples are shown and guidance provided on practical aspects of this type of large-scale stability analysis
2006
- S. J. Sherwin, R. M. Kirby, J. Peiro, R. L. Taylor and O. C. ZienkiewiczBiBTeX AbstractOn 2D Elliptic Discontinuous Galerkin MethodsInternational Journal for Numerical Methods in Engineering, 65 (5), pp. 752–784, 2006. doi 10.1002/nme.1466
@article{2006:sherwin.kirby.ea:on, author = {Sherwin, S. J. and Kirby, R. M. and Peiro, J. and Taylor, R. L. and Zienkiewicz, O. C.}, title = {On 2D Elliptic Discontinuous Galerkin Methods}, journal = {International Journal for Numerical Methods in Engineering}, year = {2006}, volume = {65}, pages = {752--784}, issue = {5}, doi = {10.1002/nme.1466}, groups = {core} }We discuss the discretization using discontinuous Galerkin (DG) formulation of an elliptic Poisson problem. Two commonly used DG schemes are investigated: the original average flux proposed by Bassi and Rebay (J. Comput. Phys. 1997; 131:267) and the local discontinuous Galerkin (LDG) (SIAM J. Numer. Anal. 1998; 35:2440) scheme. In this paper we expand on previous expositions (Discontinuous Galerkin Methods: Theory, Computation and Applications. Springer: Berlin, 2000; 135; SIAM J. Sci. Comput. 2002; 24(2):524; Int. J. Numer. Meth. Engng. 2003; 58(2): 1119) by adopting a matrix based notation with a view to highlighting the steps required in a numerical implementation of the DG method. Through consideration of standard C0-type expansion bases, as opposed to elementally orthogonal expansions, with the matrix formulation we are able to apply static condensation techniques to improve efficiency of the direct solver when high order expansions are adopted. The use of C0-type expansions also permits the direct enforcement of Dirichlet boundary conditions through a lifting approach where the LDG flux does not require further stabilization. In our construction we also adopt a formulation of the continuous DG fluxes that permits a more general interpretation of their numerical implementation. In particular it allows us to determine the conditions under which the LDG method provides a near local stencil. Finally a study of the conditioning and the size of the null space of the matrix systems resulting from the DG discretization of the elliptic problem is undertaken - R. M. Kirby and S. J. SherwinBiBTeX AbstractStabilisation of spectral/hp element methods through spectral vanishing viscosity: Application to fluid mechanics modellingComputer Methods in Applied Mechanics and Engineering, 195, pp. 3128–2144, 2006. doi 10.1016/j.cma.2004.09.019
@article{2006:kirby.sherwin:stabilisation, author = {Kirby, Robert M. and Sherwin, Spencer J.}, title = {Stabilisation of spectral/hp element methods through spectral vanishing viscosity: Application to fluid mechanics modelling}, journal = {Computer Methods in Applied Mechanics and Engineering}, year = {2006}, volume = {195}, pages = {3128--2144}, doi = {10.1016/j.cma.2004.09.019}, groups = {core} }n this paper we present a formulation of spectral vanishing viscosity (SVV) for the stabilisation of spectral/hp element methods applied to the solution of the incompressible Navier-Stokes equations. We construct the SVV around a filter with respect to an orthogonal expansions, and prove that this methodology provides a symmetric semi-positive definite SVV operator. After providing a few simple one- and two-dimensional examples to demonstrate the utility of the SVV, we examine how it can be applied to a spectral/hp element discretisation of the Navier-Stokes equations using a velocity correction splitting scheme. We provide three fluid flow examples to help illustrate the pros and cons of this approach on stability and accuracy. - R. M. Kirby and S. J. SherwinBiBTeX AbstractAliasing Errors Due to Quadratic Non-Linearities On Triangular Spectral/hp Element DiscretisationsJournal of Engineering Mathematics, 56, pp. 273–288, 2006. doi 10.1007/s10665-006-9079-5
@article{2006:kirby.sherwin:aliasing, author = {Kirby, Robert M. and Sherwin, Spencer J.}, title = {Aliasing Errors Due to Quadratic Non-Linearities On Triangular Spectral/hp Element Discretisations}, journal = {Journal of Engineering Mathematics}, year = {2006}, volume = {56}, pages = {273--288}, doi = {10.1007/s10665-006-9079-5}, groups = {core} }In this paper, consideration is given to how aliasing errors, introduced when evaluating nonlinear products, inexactly affect the solution of Galerkin spectral/hp element polynomial discretisations on triangles. A theoretical discussion is presented of how aliasing errors are introduced by a collocation projection onto a set of quadrature points insufficient for exact integration, and consider interpolation projections to geometrically symmetric ollocation points. The discussion is corroborated by numerica examples that elucidate the key features. The study is first motivated with a review of aliasing errors introduced in one-dimensional spectral-element methods (these results extend naturally to tensor-product quadrilaterals and hexahedra.) Within triangular domains two commonly used expansions are a hierarchical, or modal, expansion based on a rotationally non-symmetric collapsed-coordinate system, and a Lagrange expansion based on a set of rotationally symmetric nodal points. Whilst both expansions span the same polynomial space, the construction of the two bases numerically motivates a different set of collocation points for use in the collocation projection of a nonlinear product. The purpose of this paper is to compare these two collocation projections. The analysis and results show that aliasing errors produced using a collocation projection on the rotationally non-symmetric, collapsed-coordinate system are significantly smaller than those for a collocation projection using the rotationally symmetric nodal points. In the case of the collapsed coordinate projection, if the Gaussian quadrature order employed is less than half the polynomial order of the integrand, then it is possible for the aliasing error to modify the constant mode of the expansion and therefore affect the conservation property of the approximation. However, the use of a collocation projection onto a polynomial expansion associated with a set of rotationally symmetric nodal points within the triangle is always observed to be non-conservative. Nevertheless, the rotationally symmetric collocation will maintain the overall symmetry of the triangular region, which is not typically the case when a collapsed coordinate quadrature projection is used.
2005
- G. Karniadakis and S. SherwinSpectral/hp element methods for computational fluid dynamics. Oxford University Press, 2005. doi 10.1093/acprof:oso/9780198528692.001.0001BiBTeX Abstract
@book{2005:karniadakis.sherwin:spectralhp, author = {Karniadakis, G and Sherwin, S}, title = {Spectral/hp element methods for computational fluid dynamics}, publisher = {Oxford University Press}, year = {2005}, edition = {2nd edition}, doi = {10.1093/acprof:oso/9780198528692.001.0001}, groups = {core} }Spectral methods have long been popular in direct and large eddy simulation of turbulent flows, but their use in areas with complex-geometry computational domains has historically been much more limited. More recently, the need to find accurate solutions to the viscous flow equations around complex configurations has led to the development of high-order discretization procedures on unstructured meshes, which are also recognized as more efficient for solution of time-dependent oscillatory solutions over long time periods. This book, an updated edition on the original text, presents the recent and significant progress in multi-domain spectral methods at both the fundamental and application level. Containing material on discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilization and filtering techniques, this text introduces the use of spectral/hp element methods with particular emphasis on their application to unstructured meshes. It provides a detailed explanation of the key concepts underlying the methods along with practical examples of their derivation and application.
Applications
2025
- G. Vivarelli, J. A. Isler, C. D. Cantwell, F. Montomoli, S. J. Sherwin, Y. Frey-Marioni, M. Meyer, I. Naqavi and R. Vazquez-DiazBiBTeX AbstractA Quasi-Direct Numerical Simulation of a Compressor Blade with Separation Bubbles and Inflow TurbulenceInternational Journal of Turbomachinery, Propulsion and Power, 10 (2), p. 8, 2025. doi 10.3390/ijtpp10020008
@article{2025:vivarelli.isler.ea:quasi-direct, author = {Vivarelli, Guglielmo and Isler, Jo{\~a}o Anderson and Cantwell, Chris D and Montomoli, Francesco and Sherwin, Spencer J and Frey-Marioni, Yuri and Meyer, Marcus and Naqavi, Iftekhar and Vazquez-Diaz, Raul}, title = {A Quasi-Direct Numerical Simulation of a Compressor Blade with Separation Bubbles and Inflow Turbulence}, journal = {International Journal of Turbomachinery, Propulsion and Power}, year = {2025}, volume = {10}, number = {2}, pages = {8}, publisher = {MDPI}, groups = {app}, doi = {10.3390/ijtpp10020008} }Within the turbomachinery industry, components are currently assessed deploying standard second-order steady solvers. These are unable to capture complicated unsteady phenomena that have a critical impact on component performance. In this work, the high-order spectral h/p solver Nektar++ will be applied to a compressor blade to study the turbulent transition mechanisms and assess the effect of incoming disturbances with quasi-DNS resolution. The case will be modelled at an angle of incidence of 53.5\textdegree to match the original experimental loading at 52.8\textdegree. At clean inflow conditions, Kelvin-Helmholtz instabilities appear on both sides of the blade due to a double separation, with the pressure side one not being reported in the experiments. The separation is gradually removed by the incoming turbulent structures but at different rates on the two sides of the blade. It will be shown that there is an optimal amount of turbulence intensity that minimises momentum thickness, which is strongly related to losses. Moreover, a discussion on the spanwise extrusion will be included, this being a major player in the modelling costs. Finally, the wall-clock time and the exact expenditure to run this case will be outlined, providing quantitative evidence of the feasibility of considering a quasi-DNS resolution in an industrial setting. - P. Khurana, A. Liosi, S. Sherwin, J. Hoessler, A. Chatzopoulos, A. Swift and F. BottoneBiBTeX AbstractIndustrialization of Spectral/HP Element Method for Incompressible, Transitional Flow Around Formula 1 Geometriesin AIAA SCITECH 2025 Forum, Orlando, FL, 2025, p. 0880. doi 10.2514/6.2025-0880
@inproceedings{2025:khurana.liosi.ea:industrialization, author = {Khurana, Parv and Liosi, Alexandra and Sherwin, Spencer and Hoessler, Julien and Chatzopoulos, Athanasios and Swift, Adam and Bottone, Francesco}, title = {Industrialization of Spectral/HP Element Method for Incompressible, Transitional Flow Around Formula 1 Geometries}, booktitle = {AIAA SCITECH 2025 Forum}, year = {2025}, pages = {0880}, address = {Orlando, FL}, month = jan, organization = {American Institute of Aeronautics and Astronautics}, doi = {10.2514/6.2025-0880}, groups = {app} }This study applies the high-fidelity spectral/hp element method using the open-source Nektar++ framework to simulate the unsteady, transitional flow around complex 3D geometries representative of the Formula 1 industry. This study extends the work on a previously investigated industrial benchmark, the Imperial Front Wing (IFW), derived from the McLaren MP4-17D race car’s front wing and endplate design. A combined configuration of the IFW with a wheel in contact with a moving ground in a rolling state is considered. The rolling wheel combined with the IFW (IFW-W) provides the most realistic industrial configuration to date. The spectral/hp element method is applied to this test case to solve the incompressible Navier-Stokes equations, simulating the flow at a Reynolds number of 2.2 × 105. Time-averaged results from the unsteady simulation are compared to experimental Particle Image Velocimetry (PIV) data to assess the model’s fidelity, offering insights into its reliability for accurately representing key flow characteristics. This research addresses the challenges and requisites associated with achieving diverse levels of flow resolution using the under-resolved DNS/implicit LES approach. - A.-K. Gao, C. Xie and X.-Y. LuBiBTeXWeighted Integral Methods for Fluid Force Diagnostics in Incompressible FlowsJournal of Fluid Mechanics, 1024, p. A57, 2025. doi 10.1017/jfm.2025.10854
@article{2025:gao.xie.ea:weighted, author = {Gao, An-Kang and Xie, Chenyue and Lu, Xi-Yun}, title = {Weighted Integral Methods for Fluid Force Diagnostics in Incompressible Flows}, journal = {Journal of Fluid Mechanics}, year = {2025}, volume = {1024}, pages = {A57}, groups = {app}, doi = {10.1017/jfm.2025.10854} }
2024
- Y.-H. Xiong, A.-K. Gao, X.-Y. Lu and S. ChenBiBTeXNumerical Study of the Oscillatory Boundary Layer over Wall-Mounted Flexible FilamentsPhysical Review Fluids, 9 (12), p. 124101, 2024. doi 10.1103/PhysRevFluids.9.124101
@article{2024:xiong.gao.ea:numerical, author = {Xiong, Yu-Hang and Gao, An-Kang and Lu, Xi-Yun and Chen, Shaohua}, title = {Numerical Study of the Oscillatory Boundary Layer over Wall-Mounted Flexible Filaments}, journal = {Physical Review Fluids}, year = {2024}, volume = {9}, number = {12}, pages = {124101}, groups = {app}, doi = {10.1103/PhysRevFluids.9.124101} } - G. Vivarelli, J. A. Isler, F. Montomoli, C. Cantwell, S. J. Sherwin, Y. Frey-Marioni and R. Vazquez-DiazBiBTeX AbstractApplications and Recent Developments of the Open-Source Computational Fluid Dynamics High-Fidelity Spectral/Hp Element Framework Nektar++ for Turbomachinery ConfigurationsTurbo Expo: Power for Land, Sea, and Air, 88070, p. V12CT32A022, 2024. doi 10.1115/GT2024-125039
@article{2024:vivarelli.isler.ea:applications, author = {Vivarelli, Guglielmo and Isler, Jo{\~a}o Anderson and Montomoli, Francesco and Cantwell, Chris and Sherwin, Spencer J and Frey-Marioni, Yuri and Vazquez-Diaz, Raul}, title = {Applications and Recent Developments of the Open-Source Computational Fluid Dynamics High-Fidelity Spectral/Hp Element Framework Nektar++ for Turbomachinery Configurations}, journal = {Turbo Expo: Power for Land, Sea, and Air}, year = {2024}, volume = {88070}, pages = {V12CT32A022}, publisher = {American Society of Mechanical Engineers}, groups = {app}, doi = {10.1115/GT2024-125039} }Reynolds-Averaged-Navier-Stokes (RANS) modelling has had a significant amount of success within the industrial setting. In fact, such techniques are used on a daily basis to compute the flow field around a broad spectrum of geometries in very different conditions. To this end, many codes have now reached a good level of maturity in terms of capabilities and robustness. However, there is a growing need for more efficient designs and higher performance. Therefore, aspects that are either challenging or impossible to capture by means of standard second-order steady discretisations are starting to become of interest. The computational hardware improvements seen over the decades and the persistent development of high-order numerical techniques, are allowing Implicit Large Eddy Simulation (iLES) if not Direct Numerical Simulation (DNS). These would allow accurate capturing of unsteady flow phenomena that can be critical to properly understand aspects such as flow separation, reattachment and transition to turbulence in components relevant to the turbomachinery community. The advantage that high-order solvers, such as Nektar++, have over their standard second-order discretisation counterpart, relates to their ability to reach higher fidelity solutions with a saving in terms of number of degrees of freedom and therefore computational cost. In this paper, a detailed introduction to the characteristics and features of the open-source high-order Nektar++ Computational Fluid Dynamics (CFD) framework will be given. An initial discussion of the numerics will be provided, therefore explaining the main features of this solver, followed by a set of different capabilities that are of interest to the turbomachinery community, such as meshing, incompressible and compressible solvers and post-processing. Examples of successful deployment of these features to jet engine components will then be presented. To start, preliminary design components, such as flat plates with different loadings will be discussed. In these cases, the effects of adverse and favourable pressure gradients representative of those seen on modern engine intakes and fan blades, respectively, on boundary layers will be studied. Following, a description on low and high pressure turbine components will be provided with a discussion relating to the relevant experimental comparison. Finally, future developments and improvements to the code will be detailed, such as new schemes and interfaces to hardware enhancements, i.e. Graphical Processing Units. - D. Lindblad, J. Isler, M. M. Ginard, S. J. Sherwin and C. D. CantwellBiBTeX AbstractNektar++: Development of the compressible flow solver for jet aeroacousticsComputer Physics Communications, 300, p. 109203, 2024. doi 10.1016/j.cpc.2024.109203
@article{2024:lindblad.isler.ea:nektar, author = {Lindblad, Daniel and Isler, Jo{\~a}o and Ginard, Margarida Moragues and Sherwin, Spencer J and Cantwell, Chris D}, title = {Nektar++: Development of the compressible flow solver for jet aeroacoustics}, journal = {Computer Physics Communications}, year = {2024}, volume = {300}, pages = {109203}, publisher = {Elsevier}, groups = {app}, doi = {10.1016/j.cpc.2024.109203} }A recently developed computational framework for jet noise predictions is presented. The framework consists of two main components, focusing on source prediction and noise propagation. To compute the noise sources, the turbulent jet is simulated using the compressible flow solver implemented in the open-source spectral/hp element framework Nektar++, which solves the unfiltered Navier-Stokes equations on unstructured grids using the high-order discontinuous Galerkin method. This allows high-order accuracy to be achieved on unstructured grids, which in turn is important in order to accurately simulate industrially relevant geometries. For noise propagation, the Ffowcs Williams - Hawkings method is used to propagate the noise between the jet and the far-field. The paper provides a detailed description of the computational framework, including how the different components fit together and how to use them. To demonstrate the framework, two configurations of a single stream subsonic jet are considered. In the first configuration, the jet is treated in isolation, whereas in the second configuration, it is installed under a wing. The aerodynamic results for these two jets show strong agreement with experimental data, while some discrepancies are observed in the acoustic results, which are discussed. In addition to this, we demonstrate close to linear scaling beyond 100,000 processors on the ARCHER2 supercomputer. - K. S. Kirilov, J. Peiró, J. Zhou, M. D. Green and D. MoxeyBiBTeX AbstractHigh-Order Curvilinear Mesh Generation From Third-Party Meshesin Proceedings of the 2024 International Meshing Roundtable (IMR), 2024, pp. 93–105. doi 10.1137/1.9781611978001.8
@inbook{2024:kirilov.peiro.ea:high-order, author = {Kirilov, Kaloyan S and Peir\'o, Joaquim and Zhou, Jingtian and Green, Mashy D and Moxey, David}, title = {High-Order Curvilinear Mesh Generation From Third-Party Meshes}, pages = {93--105}, year = {2024}, booktitle = {Proceedings of the 2024 International Meshing Roundtable (IMR)}, doi = {10.1137/1.9781611978001.8}, groups = {app}, eprint = {https://epubs.siam.org/doi/pdf/10.1137/1.9781611978001.8} }Abstract Established a posteriori mesh curving techniques often rely on an accurate CAD parametrisation of the underlying mesh objects which may not always be available. To deal with such cases, we propose a method for reconstructing the missing information between the mesh and the CAD geometry when importing an arbitrarily sourced straight-sided mesh. The reconstruction is followed by curving methods for order elevation, projections and, subsequently, optimisation. Lastly, mesh modification techniques are used to achieve the desired mesh resolution and quality. We illustrate the steps of the proposed workflow through a simple geometry and a complex automotive geometry. - A.-K. Gao, Z. Chen, L. Liu and X.-Y. LuBiBTeXLift Enhancement for Airfoil at High Angle of Attack Using Flow-Induced VibrationsPhysics of Fluids, 36 (12), p. 123604, 2024. doi 10.1063/5.0240059
@article{2024:gao.chen.ea:lift, author = {Gao, An-Kang and Chen, Zhe and Liu, Luoqin and Lu, Xi-Yun}, title = {Lift Enhancement for Airfoil at High Angle of Attack Using Flow-Induced Vibrations}, journal = {Physics of Fluids}, year = {2024}, volume = {36}, number = {12}, pages = {123604}, groups = {app}, doi = {10.1063/5.0240059} } - Z. Du, A.-K. Gao, C. You, G.-Q. Chen, Y. Liu, H. Li, P. Lv and H. DuanBiBTeXRegulating Turbulent Separation by Surface Microstructures on a Blunt PlatePhysics of Fluids, 36 (5), p. 052109, 2024. doi 10.1063/5.0203964
@article{2024:du.gao.ea:regulating, author = {Du, Zengzhi and Gao, An-Kang and You, Chenxi and Chen, Guo-Qing and Liu, Yongze and Li, Hongyuan and Lv, Pengyu and Duan, Huiling}, title = {Regulating Turbulent Separation by Surface Microstructures on a Blunt Plate}, journal = {Physics of Fluids}, year = {2024}, volume = {36}, number = {5}, pages = {052109}, groups = {app}, doi = {10.1063/5.0203964} }
2023
- X.-G. Luo, A.-K. Gao and X.-Y. LuBiBTeXEnhanced Performance of a Self-Propelled Flexible Plate by a Uniform Shear Flow and Mechanism InsightPhysics of Fluids, 35 (2), p. 021903, 2023. doi 10.1063/5.0137949
@article{2023:luo.gao.ea:enhanced, author = {Luo, Xian-Guang and Gao, An-Kang and Lu, Xi-Yun}, title = {Enhanced Performance of a Self-Propelled Flexible Plate by a Uniform Shear Flow and Mechanism Insight}, journal = {Physics of Fluids}, year = {2023}, volume = {35}, number = {2}, pages = {021903}, groups = {app}, doi = {10.1063/5.0137949} } - D. Lindblad, S. J. Sherwin, C. Cantwell, J. Lawrence, A. Proenca and M. Moragues GinardBiBTeX AbstractLarge Eddy Simulations of Isolated and Installed Jet Noise using the High-Order Discontinuous Galerkin Methodin AIAA SciTech 2023 Forum, 2023, p. 1546. doi 10.2514/6.2023-1546
@inproceedings{2023:lindblad.sherwin.ea:large, author = {Lindblad, Daniel and Sherwin, Spencer J and Cantwell, Chris and Lawrence, Jack and Proenca, Anderson and Moragues Ginard, Margarida}, title = {Large Eddy Simulations of Isolated and Installed Jet Noise using the High-Order Discontinuous Galerkin Method}, booktitle = {AIAA SciTech 2023 Forum}, year = {2023}, pages = {1546}, doi = {10.2514/6.2023-1546}, groups = {app} }A recently developed computational framework for jet noise is used to compute the noise generated by an isolated and installed jet. The framework consists of two parts. In the first part, the spectral/hp element framework Nektar++ is used to compute the near-field flow. Nektar++ solves the unfiltered Navier-Stokes equations on unstructured grids using the high-order discontinuous Galerkin method. The discrete equations are integrated in time using an implicit scheme based on the matrix-free Newton-GMRES method. In the second part, the Antares library is used to compute the far-field noise. Antares solves the Ffowcs Williams - Hawkings equation for a permeable integration surface in the time domain using a source-time dominant algorithm. The simulations are validated against experimental data obtained in the Doak Laboratory Flight Jet Rig, located at the University of Southampton. For the isolated jet, good agreement is achieved, both in terms of the flow statistics and the far-field noise. The discrepancies observed for the isolated jet are believed to be caused by an under-resolved boundary layer in the simulations. For the installed jet, the flow statistics are also well predicted. In the far-field, very good agreement is achieved for downstream observers. For upstream observers, some discrepancies are observed for very high and very low frequencies. - D. Lindblad, S. J. Sherwin, C. D. Cantwell, J. Lawrence, A. Proenca and M. Moragues GinardBiBTeX AbstractAeroacoustic analysis of a closely installed chevron nozzle jet using the high-order discontinuous Galerkin methodin AIAA AVIATION 2023 Forum, 2023, p. 3831. doi 10.2514/6.2023-3831
@inproceedings{2023:lindblad.sherwin.ea:aeroacoustic, author = {Lindblad, Daniel and Sherwin, Spencer J and Cantwell, Chris D and Lawrence, Jack and Proenca, Anderson and Moragues Ginard, Margarida}, title = {Aeroacoustic analysis of a closely installed chevron nozzle jet using the high-order discontinuous Galerkin method}, booktitle = {AIAA AVIATION 2023 Forum}, year = {2023}, pages = {3831}, groups = {app}, doi = {10.2514/6.2023-3831} }In this paper, we use Large Eddy Simulations (LES) in combination with the Ffowcs Williams - Hawkings method to study the influence of chevrons on the flow field as well as the noise produced by a closely installed M = 0.6 jet. The LES simulations are performed with the spectral/hp element framework Nektar++. Nektar++ uses the high-order discontinuous Galerkin method and an implicit scheme based on the matrix-free Newton-GMRES method to discretize the unfiltered Navier-Stokes equations in space and time, respectively. The far-field noise is computed using Antares. Antares solves the Ffowcs Williams - Hawkings equation for a permeable integration surface in the time-domain using a source-time dominant algorithm. The aerodynamic results show good agreement with experimental data obtained in the Doak Laboratory Flight Jet Rig, located at the University of Southampton. Some discrepancies are observed in terms of the far-field noise levels, especially for higher polar observer angles relative to the downstream jet axis. In terms of noise reduction potential, the simulations predict that the chevrons reduce the OASPL by 1dB compared to an installed round nozzle for all observers located on the unshielded side of the wing. This should be compared to the experiments, which predict a 1.5dB noise reduction for the same chevron nozzle. - D. Lindblad, J. Isler, M. Moragues, S. J. Sherwin and C. D. CantwellBiBTeX AbstractNektar++: Development of the Compressible Flow Solver for Large Scale Aeroacoustic Applications2023. doi 10.1016/j.cpc.2024.109203
@article{2023:lindblad.isler.ea:nektar, author = {Lindblad, D and Isler, J and Moragues, M and Sherwin, SJ and Cantwell, C. D.}, title = {{Nektar++}: {Development} of the Compressible Flow Solver for Large Scale Aeroacoustic Applications}, year = {2023}, doi = {10.1016/j.cpc.2024.109203}, groups = {app} }A recently developed computational framework for jet noise predictions is presented. The framework consists of two main components, focusing on source prediction and noise propagation. To compute the noise sources, the turbulent jet is simulated using the compressible flow solver implemented in the open-source spectral/hp element framework Nektar++, which solves the unfiltered Navier-Stokes equations on unstructured grids using the high-order discontinuous Galerkin method. This allows high-order accuracy to be achieved on unstructured grids, which in turn is important in order to accurately simulate industrially relevant geometries. For noise propagation, the Ffowcs Williams - Hawkings method is used to propagate the noise between the jet and the far-field. The paper provides a detailed description of the computational framework, including how the different components fit together and how to use them. To demonstrate the framework, two configurations of a single stream subsonic jet are considered. In the first configuration, the jet is treated in isolation, whereas in the second configuration, it is installed under a wing. The aerodynamic results for these two jets show strong agreement with experimental data, while some discrepancies are observed in the acoustic results, which are discussed. In addition to this, we demonstrate close to linear scaling beyond processors on the ARCHER2 supercomputer. - D. S. Lampropoulos, I. D. Boutopoulos, G. C. Bourantas, K. Miller, P. E. Zampakis and V. C. LoukopoulosBiBTeX AbstractHemodynamics of anterior circulation intracranial aneurysms with daughter blebs: investigating the multidirectionality of blood flow fieldsComputer Methods in Biomechanics and Biomedical Engineering, 26 (1), pp. 113–125, 2023. doi 10.1080/10255842.2022.2048374
@article{2023:lampropoulos.boutopoulos.ea:hemodynamics, author = {Lampropoulos, Dimitrios S and Boutopoulos, Ioannis D. and Bourantas, George C. and Miller, Karol and Zampakis, Petros E. and Loukopoulos, Vassilios C.}, title = {Hemodynamics of anterior circulation intracranial aneurysms with daughter blebs: investigating the multidirectionality of blood flow fields}, journal = {Computer Methods in Biomechanics and Biomedical Engineering}, year = {2023}, volume = {26}, number = {1}, pages = {113--125}, note = {PMID: 35297711}, publisher = {Taylor \& Francis}, doi = {10.1080/10255842.2022.2048374}, eprint = {https://doi.org/10.1080/10255842.2022.2048374}, groups = {app} }Recent advances in diagnostic neuroradiological imaging, allowed the detection of unruptured intracranial aneurysms (IAs). The shape - irregular or multilobular - of the aneurysmal dome, is considered as a possible rupture risk factor, independently of the size, the location and patient medical background. Disturbed blood flow fields in particular is thought to play a key role in IAs progression. However, there is an absence of widely-used hemodynamic indices to quantify the extent of a multi-directional disturbed flow. We simulated blood flow in twelve patient-specific anterior circulation unruptured intracranial aneurysms with daughter blebs utilizing the spectral/hp element framework Nektar++. We simulated three cardiac cycles using a volumetric flow rate waveform while we considered blood as a Newtonian fluid. To investigate the multidirectionality of the blood flow fields, besides the time-averaged wall shear stress (TAWSS), we calculated the oscillatory shear index (OSI), the relative residence time (RRT) and the time-averaged cross flow index (TACFI). Our CFD simulations suggest that in the majority of our vascular models there is a formation of complex intrasaccular flow patterns, resulting to low and highly oscillating WSS, especially in the area of the daughter blebs. The existence of disturbed multi-directional blood flow fields is also evident by the distributions of the RRT and the TACFI. These findings further support the theory that IAs with daughter blebs are linked to a potentially increased rupture risk. - M. Lahooti, Y. Bao, D. Scott, R. Palacios and S. J. SherwinBiBTeX AbstractLES/DNS fluid-structure interaction simulation of non-linear slender structures in Nektar++ frameworkComputer Physics Communications, 282, p. 108528, 2023. doi 10.1016/j.cpc.2022.108528
@article{2023:lahooti.bao.ea:lesdns, author = {Lahooti, Mohsen and Bao, Yan and Scott, David and Palacios, Rafael and Sherwin, Spencer J}, title = {{LES/DNS} fluid-structure interaction simulation of non-linear slender structures in {Nektar++} framework}, journal = {Computer Physics Communications}, year = {2023}, volume = {282}, pages = {108528}, publisher = {Elsevier}, groups = {app}, doi = {10.1016/j.cpc.2022.108528} }Nektar++ is a spectral/hp element open-source framework written in C++ for the construction of classical low-order h-type as well as higher-order p-type finite element solvers. It seeks to overcome the implementation challenges of the complex data structures associated with high-order finite element methods; hence, providing an efficient, flexible and HPC scalable platform for the development of solvers for partial differential equations using the spectral/hp element method. In the present work, capabilities of Nektar++ is leveraged for development of two fluid-structure interaction (FSI) solvers for simulations of highly deformable nonlinear slender structures. The FSI solver uses the incompressible Navier-Stokes (NS) solvers of Nektar++ for fluid flow while the structural dynamics is modelled using Geometrically-Exact Composite Beams (GECB). The open-source SHARPy framework is linked to Nektar++ and used for structural simulation. Aiming at high-fidelity (LES/DNS) FSI simulations, the thick-strip approach is used to reduce computational costs. In this approach, the full 3D fluid domain is represented with series of smaller 3D domains normal to the local axis of the structure and having a finite thickness in the spanwise direction where periodicity is also assumed. Hence, while reducing the computational costs by avoiding the discretization of equations over the entire slender structure, the strip thickness allows capturing the local 3D turbulent wake and accurately predict the fluid forces on the structure. Two approaches are adopted to avoid the dynamic remeshing due to the large and non-linear deformation of the structure. In the first approach, the transformed the NS equations are solved in the non-inertial body-fitted coordinates while in the second approach the NS equations are formulated in the moving frame of reference and solved with the spectral/hp element method. A hybrid parallelisation approach of Nektar++ is extended for the thick-strip method which allows having non-constant cross-section along the structural span as well as efficient and flexible use of computational resources, and excellent HPC performance for the FSI simulations. The capability of the FSI solver is demonstrated via several examples. - K. S. Kirilov, J. Peiró, J. Zhou, M. D. Green and D. MoxeyBiBTeX AbstractA workflow for generating high-order meshes by curving third-party meshes, and assessing their quality and geometrical accuracy for industrial applicationsin Proceedings of the International Conference on Spectral and High Order Methods (ICOSAHOM 2023), 2023. doi 10.1007/978-3-031-76988-7_15
@inproceedings{2023:kirilov.peiro.ea:workflow, author = {Kirilov, Kaloyan S. and Peir\'o, Joaquim and Zhou, Jingtian and Green, Mashy D. and Moxey, David}, title = {A workflow for generating high-order meshes by curving third-party meshes, and assessing their quality and geometrical accuracy for industrial applications}, booktitle = {Proceedings of the International Conference on Spectral and High Order Methods (ICOSAHOM 2023)}, year = {2023}, doi = {10.1007/978-3-031-76988-7_15}, groups = {app} }Simulating industrial flows involving complex geometries with high-order CFD methods requires good-quality curvilinear meshes to ensure their accuracy, stability and computational efficiency. We describe a modification of the high-order mesh generator NekMesh to allow the curving of straight-sided meshes generated by third-party software to benefit from their robustness and flexibility. We propose further a modified workflow that maintains mesh conformity to the underlying CAD (B-rep) model, but most importantly it allows us to assess the geometrical accuracy and its potential impact on the flow simulation. Application to a simple benchmark test and a complex automotive geometry will demonstrate the suitability of the modified workflow and the resulting mesh quality. - L. Kang, A.-K. Gao, F. Han, W. Cui and X.-Y. LuBiBTeXPropulsive Performance and Vortex Dynamics of Jellyfish-like Propulsion with Burst-and-Coast StrategyPhysics of Fluids, 35 (9), p. 091904, 2023. doi 10.1063/5.0160878
@article{2023:kang.gao.ea:propulsive, author = {Kang, Linlin and Gao, An-Kang and Han, Fei and Cui, Weicheng and Lu, Xi-Yun}, title = {Propulsive Performance and Vortex Dynamics of Jellyfish-like Propulsion with Burst-and-Coast Strategy}, journal = {Physics of Fluids}, year = {2023}, volume = {35}, number = {9}, pages = {091904}, groups = {app}, doi = {10.1063/5.0160878} } - A.-K. Gao, C. D. Cantwell, O. Son and S. J. SherwinBiBTeX AbstractThree-dimensional transition and force characteristics of low-Reynolds-number flows past a plunging airfoilJournal of Fluid Mechanics, 973, p. A43, 2023. doi 10.1017/jfm.2023.735
@article{2023:gao.cantwell.ea:three-dimensional, author = {Gao, An-Kang and Cantwell, Chris D and Son, Onur and Sherwin, Spencer J}, title = {Three-dimensional transition and force characteristics of low-Reynolds-number flows past a plunging airfoil}, journal = {Journal of Fluid Mechanics}, year = {2023}, volume = {973}, pages = {A43}, publisher = {Cambridge University Press}, groups = {app}, doi = {10.1017/jfm.2023.735} }The three-dimensional (3-D) transition of the leading-edge vortex (LEV) and the force characteristics of the plunging airfoil are investigated in the chord-based Strouhal number Stc range of 0.10 to 1.0 by means of experimental measurements, numerical simulations and linear stability analysis in order to understand the spanwise instabilities and the effects on the force. We find that the interaction pattern of the LEV, the LEV from a previous cycle (pLEV) and the trailing-edge vortex (TEV) is the primary mechanism that affects the 3-D transition and associated force characteristics. For Stc≤0.16, the 3-D transition is dominated by the LEV-TEV interaction. For 0.16<Stc≤0.44, the TEV lies in the middle of the LEV and the pLEV and therefore vortex interaction between them is relatively weak; as a result, the LEV remains two-dimensional up to a relatively high Reynolds number of Re=4000 at Stc=0.32. For 0.44<Stc≤0.54, and at relatively low Reynolds numbers, the pLEV and the TEV tend to form a clockwise vortex pair, which is beneficial for the high lift and stability of the LEV. For 0.49\leqStc, the pLEV and TEV tend to form an anticlockwise vortex pair, which is detrimental to the lift and flow stability. In the last Stc$ range, vortex interaction involving the LEV, the TEV and the pLEV results in an unstable period-doubling mode which has a wavelength of about two chord-lengths and the 3-D transition enhances the lift.
2022
- O. Son, A.-K. Gao, I. Gursul, C. D. Cantwell, Z. Wang and S. J. SherwinBiBTeXLeading-Edge Vortex Dynamics on Plunging Airfoils and WingsJournal of Fluid Mechanics, 940, p. A28, 2022. doi 10.1017/jfm.2022.224
@article{2022:son.gao.ea:leading-edge, author = {Son, O. and Gao, A.-K. and Gursul, I. and Cantwell, C.D. and Wang, Z. and Sherwin, S.J.}, title = {Leading-Edge Vortex Dynamics on Plunging Airfoils and Wings}, journal = {Journal of Fluid Mechanics}, year = {2022}, volume = {940}, pages = {A28}, groups = {app}, doi = {10.1017/jfm.2022.224} } - G. Lyu, C. Chen, X. Du, M. S. Mughal and S. J. SherwinBiBTeX AbstractOpen-source framework for transonic boundary layer natural transition analysis over complex geometries in Nektar++in AIAA AVIATION 2022 Forum, 2022, p. 4032. doi 10.48550/arXiv.2201.05404
@inproceedings{2022:lyu.chen.ea:open-source, author = {Lyu, Ganlin and Chen, Chao and Du, Xi and Mughal, Mohammed S and Sherwin, Spencer J}, title = {Open-source framework for transonic boundary layer natural transition analysis over complex geometries in {Nektar++}}, booktitle = {AIAA AVIATION 2022 Forum}, year = {2022}, pages = {4032}, groups = {app}, doi = {10.48550/arXiv.2201.05404} }In this paper, we present recent efforts to develop reduced order modeling (ROM) capabilities for spectral element methods (SEM). Namely, we detail the implementation of ROM for both continuous Galerkin and discontinuous Galerkin methods in the spectral/hp element library Nektar++. The ROM approaches adopted are intrusive methods based on the proper orthogonal decomposition (POD). They admit an offline-online decomposition, such that fast evaluations for parameter studies and many-queries are possible. An affine parameter dependency is exploited such that the reduced order model can be evaluated independent of the large-scale discretization size. The implementation in the context of SEM can be found in the open-source model reduction software ITHACA-SEM. - B. Liu, C. D. Cantwell, D. Moxey, G. Mashy and S. J. SherwinBiBTeX AbstractVectorised spectral/hp element matrix-free operator for anisotropic heat transport in tokamak edge plasmain 8th European Congress on Computational Methods in Applied Sciences and Engineering, 2022. doi 10.23967/eccomas.2022.291
@inproceedings{2022:liu.cantwell.ea:vectorised, author = {Liu, Bin and Cantwell, CD and Moxey, David and Mashy, G and Sherwin, SJ}, title = {Vectorised spectral/$hp$ element matrix-free operator for anisotropic heat transport in tokamak edge plasma}, booktitle = {8th European Congress on Computational Methods in Applied Sciences and Engineering}, year = {2022}, organization = {Newcastle University}, groups = {app}, doi = {10.23967/eccomas.2022.291} }A highly efficient matrix-free Helmholtz operator with single-instruction multipledata (SIMD) vectorisation is implemented in Nektar++ and applied to the simulation of anisotropic heat transport in tokamak edge plasma. A tokamak is currently the leading candidate for a practical fusion reactor using the magnetic confinement approach to produce electricity through controlled thermonuclear fusion. Predicting the transport of heat in magnetized plasma is important to designing a safe tokamak design. Due to the ionized nature of plasma, the heat conduction of the magnetized plasma is highly anisotropic along the magnetic field lines. In this study, a variational form is proposed to simulate the anisotropic heat transport in magnetized plasma and the details of its mathematical derivation and implementation are presented. To accurately approximate the thermal load of plasma deposition on the wall of tokamak chamber, highly scalable and efficient algorithms are crucial. To achieve this, a matrix-free Helmholtz operator is implemented in the Nektar++ framework, utilising sum-factorisation to reduce the operation count and increase arithmetic intensity, and leveraging SIMD vectorisation to accelerate the computation on modern hardware. The performance of the implementation is assessed by measuring throughput and speed-up of the operators using deformed and regular quadrilateral and triangular elements. - M. Lino, S. Fotiadis, A. A. Bharath and C. CantwellBiBTeX AbstractREMuS-GNN: A rotation-equivariant model for simulating continuum dynamicsin Topological, Algebraic and Geometric Learning Workshops 2022, 2022, pp. 226–236. doi 10.48550/arXiv.2205.07852
@inproceedings{2022:lino.fotiadis.ea:remus-gnn, author = {Lino, Mario and Fotiadis, Stathi and Bharath, Anil A and Cantwell, Chris}, title = {REMuS-GNN: A rotation-equivariant model for simulating continuum dynamics}, booktitle = {Topological, Algebraic and Geometric Learning Workshops 2022}, year = {2022}, pages = {226--236}, organization = {PMLR}, groups = {app}, doi = {10.48550/arXiv.2205.07852} }Numerical simulation is an essential tool in many areas of science and engineer- ing, but its performance often limits application in practice or when used to ex- plore large parameter spaces. On the other hand, surrogate deep learning models, while accelerating simulations, often exhibit poor accuracy and ability to gen- eralise. In order to improve these two factors, we introduce REMuS-GNN, a rotation-equivariant multi-scale model for simulating continuum dynamical sys- tems encompassing a range of length scales. REMuS-GNN is designed to predict an output vector field from an input vector field on a physical domain discretised into an unstructured set of nodes. Equivariance to rotations of the domain is a desirable inductive bias that allows the network to learn the underlying physics more efficiently, leading to improved accuracy and generalisation compared with similar architectures that lack such symmetry. We demonstrate and evaluate this method on the incompressible flow around elliptical cylinders - M. Lino, S. Fotiadis, A. A. Bharath and C. D. CantwellBiBTeX AbstractMulti-scale rotation-equivariant graph neural networks for unsteady Eulerian fluid dynamicsPhysics of Fluids, 34 (8), 2022. doi 10.1063/5.0097679
@article{2022:lino.fotiadis.ea:multi-scale, author = {Lino, Mario and Fotiadis, Stathi and Bharath, Anil A and Cantwell, Chris D}, title = {Multi-scale rotation-equivariant graph neural networks for unsteady Eulerian fluid dynamics}, journal = {Physics of Fluids}, year = {2022}, volume = {34}, number = {8}, publisher = {AIP Publishing}, groups = {app}, doi = {10.1063/5.0097679} }The simulation of fluid dynamics, typically by numerically solving partial differential equations, is an essential tool in many areas of science and engineering. However, the high computational cost can limit application in practice and may prohibit exploring large parameter spaces. Recent deep-learning approaches have demonstrated the potential to yield surrogate models for the simulation of fluid dynamics. While such models exhibit lower accuracy in comparison, their low runtime makes them appealing for design-space exploration. We introduce two novel graph neural network (GNN) models, multi-scale (MuS)-GNN and rotation-equivariant (RE) MuS-GNN, for extrapolating the time evolution of the fluid flow. In both models, previous states are processed through multiple coarsening of the graph, which enables faster information propagation through the network and improves the capture and forecast of the system state, particularly in problems encompassing phenomena spanning a range of length scales. Additionally, REMuS-GNN is architecturally equivariant to rotations, which allows the network to learn the underlying physics more efficiently, leading to improved accuracy and generalization. We analyze these models using two canonical fluid models: advection and incompressible fluid dynamics. Our results show that the proposed GNN models can generalize from uniform advection fields to high-gradient fields on complex domains. The multi-scale graph architecture allows for inference of incompressible Navier-Stokes solutions, within a range of Reynolds numbers and design parameters, more effectively than a baseline single-scale GNN. Simulations obtained with MuS-GNN and REMuS-GNN are between two and four orders of magnitude faster than the numerical solutions on which they were trained. - D. Lindblad, S. Sherwin, C. Cantwell, J. Lawrence, A. Proenca and M. Moragues GinardBiBTeX AbstractAeroacoustic analysis of a subsonic jet using the discontinuous Galerkin methodin 28th AIAA/CEAS Aeroacoustics 2022 Conference, 2022, p. 2932. doi 10.2514/6.2022-2932
@inproceedings{2022:lindblad.sherwin.ea:aeroacoustic, author = {Lindblad, Daniel and Sherwin, Spencer and Cantwell, Chris and Lawrence, Jack and Proenca, Anderson and Moragues Ginard, Margarida}, title = {Aeroacoustic analysis of a subsonic jet using the discontinuous {Galerkin} method}, booktitle = {28th AIAA/CEAS Aeroacoustics 2022 Conference}, year = {2022}, pages = {2932}, groups = {app}, doi = {10.2514/6.2022-2932} }In this work, the open-source spectral/hp element framework Nektar++ is coupled with the Antares library to predict noise from a subsonic jet. Nektar++ uses the high-order discontinuous Galerkin method to solve the compressible Navier-Stokes equations on unstructured grids. Unresolved turbulent scales are modeled using an implicit Large Eddy Simulation approach. In this approach, the favourable dissipation properties of the discontinuous Galerkin method are used to remove the highest resolved wavenumbers from the solution. For time-integration, an implicit, matrix-free, Newton-Krylov method is used. To compute the far-field noise, Antares solves the Ffowcs Williams - Hawkings equation for a permeable integration surface in the time-domain using a source-time dominant algorithm. The simulation results are validated against experimental data obtained in the Doak Laboratory Flight Jet Rig, located at the University of Southampton. - A.-K. GaoBiBTeX AbstractLeading-edge vortex dynamics on plunging airfoils and wingsJournal of Fluid Mechanics, 940, p. A28, 2022. doi 10.1017/jfm.2022.224
@article{2022:gao:leading-edge, author = {Gao, A-K}, title = {Leading-edge vortex dynamics on plunging airfoils and wings}, journal = {Journal of Fluid Mechanics}, year = {2022}, volume = {940}, pages = {A28}, publisher = {Cambridge University Press}, groups = {app}, doi = {10.1017/jfm.2022.224} }The vortex dynamics of leading-edge vortices on plunging high-aspect-ratio (AR = 10) wings and airfoils were investigated by means of volumetric velocity measurements, numerical simulations and stability analysis to understand the deformation of the leading-edge vortex filament and spanwise instabilities. The vortex filaments on both the wing and airfoil exhibit spanwise waves, but with different origins. The presence of a wing-tip causes the leg of the vortex to remain attached to the wing upper surface, while the initial deformation of the filament near the wing tip resembles a helical vortex. The essential features can be modelled as the deformation of an initially L-shaped semi-infinite vortex column. In contrast, the instability of the vortices is well captured by the instability of counter-rotating vortex pairs, which are formed either by the trailing-edge vortices or the secondary vortices rolled-up from the wing surface. The wavelengths observed in the experiments and simulations are in agreement with the stability analysis of counter-rotating vortex pairs of unequal strength.
2021
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@article{2021:proskurin.sagalakov:simple, author = {Proskurin, AV and Sagalakov, AM}, title = {A simple scenario of the laminar breakdown in liquid metal flows}, journal = {Magnetohydrodynamics}, year = {2021}, volume = {57}, number = {2}, groups = {app}, url = {https://mhd.sal.lv/Download/download-opac_V60N1A7.php?ed=rn&vol=57&nr=2&an=5&p1=191&p2=191} }In the article, authors present a numerical method for modelling a laminar-turbulent transition in magnetohydrodynamic flows. The small magnetic Reynolds number approach is considered. Velocity, pressure and electrical potential are decomposed to the sum of state values and finite amplitude perturbations. A solver based on the Nektar++ framework is described. The authors suggest using small-length local perturbations as a transition trigger. They can be imposed by blowing or by electrical enforcing. The stability of the Hartmann flow and the flow in the bend are considered as examples. Tables 4, Figs 19, Refs 28 - H. Jiang, X. Ju and Y. LuBiBTeX AbstractLarge-Eddy Simulation of Flow Past a Circular Cylinder Using OpenFOAM and Nektar++in International Conference on Offshore Mechanics and Arctic Engineering, 2021, 85185, p. V008T08A019. doi 10.1115/OMAE2021-61392
@inproceedings{2021:jiang.ju.ea:large-eddy, author = {Jiang, Hongyi and Ju, Xiaoying and Lu, Yucen}, title = {Large-Eddy Simulation of Flow Past a Circular Cylinder Using {OpenFOAM} and {Nektar++}}, booktitle = {International Conference on Offshore Mechanics and Arctic Engineering}, year = {2021}, volume = {85185}, pages = {V008T08A019}, organization = {American Society of Mechanical Engineers}, groups = {app}, doi = {10.1115/OMAE2021-61392} }Steady incoming flow past a circular cylinder has been a classical problem in fluid mechanics owing to its extensive practical applications in e.g. offshore engineering. In this study, large-eddy simulations are performed for flow past a circular cylinder at the Reynolds number (Re) of 3900. Particular focuses are on the comparisons of different numerical methods and computational domain patterns. The case Re = 3900 is computed with both OpenFOAM and Nektar++, which are based on the conventional finite volume method and the highorder spectral/hp element method, respectively. It is found that the computational cost for the Nektar++ model is only less than 10% of that for the OpenFOAM model. In addition, both circular and C-shaped domains are tested for the OpenFOAM and Nektar++ models. It is found that a circular domain is required for the OpenFOAM model to minimise the footprint of mesh non-orthogonality on the simulated flow, while the Nektar++ model does not have strict requirements for the orthogonality of the mesh. The present findings regarding the computational cost and the domain/mesh patterns are expected to be applicable to the numerical modelling of bluff-body flows in general. Based on Nektar++ and the circular domain, additional simulations are performed at Re = 1000 and 7000. For the three Re values investigated, the Strouhal number, hydrodynamic forces and the streamwise and spanwise vorticity fields are examined and compared. - M. Z. Hossain, C. D. Cantwell and S. J. SherwinBiBTeX AbstractA spectral/hp element method for thermal convectionInternational Journal for Numerical Methods in Fluids, 93 (7), pp. 2380–2395, 2021. doi 10.1002/fld.4978
@article{2021:hossain.cantwell.ea:spectralhp, author = {Hossain, Mohammad Z and Cantwell, Chris D and Sherwin, Spencer J}, title = {A spectral/$hp$ element method for thermal convection}, journal = {International Journal for Numerical Methods in Fluids}, year = {2021}, volume = {93}, number = {7}, pages = {2380--2395}, publisher = {Wiley Online Library}, groups = {app}, doi = {10.1002/fld.4978} }We report on a high-fidelity, spectral/hp element algorithm developed for the direct numerical simulation of thermal convection problems. We consider the incompressible Navier-Stokes (NS) and advection-diffusion equations coupled through a thermal body-forcing term. The flow is driven by a prescribed flowrate forcing with explicit treatment of the nonlinear advection terms. The explicit treatment of the body-force term also decouples both the NS and the advection-diffusion equations. The problem is then temporally discretized using an implicit-explicit scheme in conjunction with a velocity-correction splitting scheme to decouple the velocity and pressure fields in the momentum equation. Although not unique, this type of discretization has not been widely applied to thermal convection problems and we therefore provide a comprehensive overview of the algorithm and implementation which is available through the open-source package Nektar++. After verifying the algorithm on a number of illustrative problems we then apply the code to investigate flow in a channel with uniform or streamwise sinusoidal lower wall, in addition to a patterned sinusoidal heating. We verify the solver against previously published two-dimensional results. Finally, for the first time we consider a three-dimensional problem with a streamwise sinusoidal lower wall and sinusoidal heating which, for the chosen parameter, leads to the unusual dynamics of an initially unsteady two-dimensional instability leading to a steady three-dimensional nonlinear saturated state.
2020
- C. Xiong, X. Qi, A. Gao, H. Xu, C. Ren and L. ChengBiBTeXThe Bypass Transition Mechanism of the Stokes Boundary Layer in the Intermittently Turbulent RegimeJournal of Fluid Mechanics, 896, p. A4, 2020. doi 10.1017/jfm.2020.313
@article{2020:xiong.qi.ea:bypass, author = {Xiong, Chengwang and Qi, Xiang and Gao, Ankang and Xu, Hui and Ren, Chengjiao and Cheng, Liang}, title = {The Bypass Transition Mechanism of the {{Stokes}} Boundary Layer in the Intermittently Turbulent Regime}, journal = {Journal of Fluid Mechanics}, year = {2020}, volume = {896}, pages = {A4}, groups = {app}, doi = {10.1017/jfm.2020.313} } - Mejı́a Manuel F, D. Serson, R. C. Moura, B. S. Carmo, J. Escobar-Vargas and A. González-ManceraBiBTeXErosion Wear Evaluation Using Nektar++in Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018: Selected Papers from the ICOSAHOM Conference, London, UK, July 9-13, 2018, 2020, pp. 419–428. doi 10.1007/978-3-030-39647-3_33
@inproceedings{2020:meja.serson.ea:erosion, author = {Mej{\'\i}a, Manuel F and Serson, Douglas and Moura, Rodrigo C and Carmo, Bruno S and Escobar-Vargas, Jorge and Gonz{\'a}lez-Mancera, Andr{\'e}s}, title = {Erosion Wear Evaluation Using Nektar++}, booktitle = {Spectral and High Order Methods for Partial Differential Equations {ICOSAHOM 2018}: Selected Papers from the {ICOSAHOM} Conference, London, UK, July 9-13, 2018}, year = {2020}, pages = {419--428}, organization = {Springer International Publishing}, groups = {app}, doi = {10.1007/978-3-030-39647-3_33} } - G. Guo, J. Gong and M. ZhangBiBTeX AbstractNumerical investigation on flow characteristics of low-speed flow over a cavity with small aspect ratioInternational Journal of Mechanical Sciences, 178, p. 105632, 2020. doi 10.1016/j.ijmecsci.2020.105632
@article{2020:guo.gong.ea:numerical, author = {Guo, Guangming and Gong, Junjie and Zhang, Mengqi}, title = {Numerical investigation on flow characteristics of low-speed flow over a cavity with small aspect ratio}, journal = {International Journal of Mechanical Sciences}, year = {2020}, volume = {178}, pages = {105632}, publisher = {Elsevier}, groups = {app}, doi = {10.1016/j.ijmecsci.2020.105632} }Numerical simulations of low-speed flow over a two-dimensional cavity at different cavity length-to-depth ratio (R) and freestream Reynolds number (Re) are performed by using the Nektar++ method. This work focuses on flow characteristics of vortices inside cavity, such as evolution process, number, and velocity due to variations in the R and Re. From the evolution process shown by the cavity flow at R = 1 and Re = 1612, it was found that both the main and corner vortices originate from the wall vortex appeared on the cavity wall, and the main vortex reaches stable faster than two corner vortices. There are seven vortices of similar size and shape arranged vertically inside the cavity for the case of R = 0.1 and Re = 1612, number of these vortices decreases to one while velocity of fluid inside the cavity increases gradually as the R increases from 0.1 to 0.9. The increase of Re results in more vortices and a larger velocity of fluid inside the cavity, furthermore, a sequence of small-scale vortical structures downstream of the cavity trailing edge are generated under the condition of Re = 25792. In addition, sidewall effects on cavity flow characteristics are investigated by employing a three-dimensional cavity, and the analysis shown that sidewall effects on flow pattern of fluid in the spanwise plane near the sidewall are not negligible. - Fürst Jiřı́, M. Lasota, J. Musil and J. PechBiBTeX AbstractNumerical Investigation of Aeroelastic Flutter in Two-Dimensional Cascade of Compressor Bladesin MATEC Web of Conferences, 2020, 328, p. 02020. doi 10.1051/matecconf/202032802020
@inproceedings{2020:furst.lasota.ea:numerical, author = {F{\"u}rst, Ji{\v{r}}{\'\i} and Lasota, Martin and Musil, Josef and Pech, Jan}, title = {Numerical Investigation of Aeroelastic Flutter in Two-Dimensional Cascade of Compressor Blades}, booktitle = {MATEC Web of Conferences}, year = {2020}, volume = {328}, pages = {02020}, organization = {EDP Sciences}, groups = {app}, doi = {10.1051/matecconf/202032802020} }Following contribution presents numerical study of aeroelastic flutter in two-dimensional section of flat wing cascade in wind tunnel. The investigation is conducted as a parametric study of varying pitch angle of one (middle) blade in the cascade with each computational case performed on fixed computational grid. This approach can be viewed as an approximation of fluid-structure interaction realized on moving mesh. Numerical predictions were carried by means of CFD open-source codes OpenFOAM and Nektar++. The particular aim was focused on assessment of numerical performance and accuracy of the numerical solvers as well as several turbulence models. - F. F. Buscariolo, W. Hambli, J. Slaughter and S. SherwinBiBTeX AbstractUsing a spectral/hp element method for high-order implicit-LES of bluff automotive geometries2020. doi 10.17028/rd.lboro.12102594.v1
@article{2020:buscariolo.hambli.ea:using, author = {Buscariolo, Filipe Fabian and Hambli, Walid and Slaughter, James and Sherwin, Spencer}, title = {Using a spectral/$hp$ element method for high-order implicit-{LES} of bluff automotive geometries}, year = {2020}, publisher = {Loughborough University}, groups = {app}, doi = {10.17028/rd.lboro.12102594.v1} }The combination of High-order methods and Large-Eddy Simulation (LES) is an ongoing research focus in turbulence due to the attractive dissipation characteristics of high-order methods. Whilst numerically speaking these methodologies are advantageous, their application is inhibited on industrial cases due to the inherent geometric complexities of such problems. Spectral/hp Element (SEM) solvers such as Nektar++, have potential to be bridge the gap between high-order methods and industrial geometric complexity. This study focuses on the intersection of the application of the SEM solver Nektar++ to an automotive geometry as well as the presentation of high-order mean flow characteristics for the SAE Notchback body. Using a 5th order polynomial expansion at ReL = 2.3 × 106 on a curvilinear grid, results are compared with those empirically achieved in other works. Implicit Sub-Grid scale modelling along with a novel Spectral-Vanishing Viscosity (SVV) approach is employed acting as an artificial diffusion operator preventing high-frequency instabilities and spurious oscillations. Suitable qualitative agreement between PIV and CFD methods is obtained, and quantitative agreement is demonstrated on CD with 9% difference. More extensive backlight separation and subsequent bootlid impingement is observed in CFD than presented in the literature. This might be caused due to differing inflow characteristics, resulting in CM and CL variance to experimental values. Along with the mean flow field characteristics, the methodology and the pipeline used to achieve such results and agreement is presented. The use of a wall-conforming unstructured curvilinear grid allows for significantly greater geometric flexibility whilst retaining the advantages of the high-order polynomial expansion.
2019
- A.-K. Gao, S.-F. Zou, Y. Shi and J. Z. WuBiBTeXPassing-over Leading-Edge Vortex: The Thrust Booster in Heaving AirfoilAIP Advances, 9 (3), p. 035314, 2019. doi 10.1063/1.5064696
@article{2019:gao.zou.ea:passing-over, author = {Gao, An-Kang and Zou, Shu-Fan and Shi, Yipeng and Wu, J. Z.}, title = {Passing-over Leading-Edge Vortex: {{The}} Thrust Booster in Heaving Airfoil}, journal = {AIP Advances}, year = {2019}, volume = {9}, number = {3}, pages = {035314}, groups = {app}, doi = {10.1063/1.5064696} } - A.-K. Gao and J. WuBiBTeXA Note on the Galilean Invariance of Aerodynamic Force Theories in Unsteady Incompressible FlowsActa Mechanica Sinica, 35 (6), pp. 1150–1154, 2019. doi 10.1007/s10409-019-00896-5
@article{2019:gao.wu:note, author = {Gao, An-Kang and Wu, Jiezhi}, title = {A Note on the {{Galilean}} Invariance of Aerodynamic Force Theories in Unsteady Incompressible Flows}, journal = {Acta Mechanica Sinica}, year = {2019}, volume = {35}, number = {6}, pages = {1150--1154}, groups = {app}, doi = {10.1007/s10409-019-00896-5} } - J. Eichstädt, D. Moxey and J. PeiróBiBTeX AbstractTowards a performance-portable high-order implicit flow solverin 2019 AIAA Aerospace Sciences Meeting, 2019. doi 10.2514/6.2019-1404
@inproceedings{2019:eichstadt.moxey.ea:towards, author = {Eichst\"adt, J. and Moxey, D. and Peir\'o, J.}, title = {Towards a performance-portable high-order implicit flow solver}, booktitle = {2019 AIAA Aerospace Sciences Meeting}, year = {2019}, doi = {10.2514/6.2019-1404}, groups = {app} }We discuss the steps required to adapt legacy flow, or structural, solvers to modern CPU and GPU architectures using a portable programming model. These steps are illustrated using a high-order mesh optimiser and an implicit Helmholtz solver as examples. We show that satisfactory performance can be achieved in both architectures using such a framework, and highlight the importance of developing efficient data structures.
2018
- D. Xin, H. Zhang and J. OuBiBTeX AbstractSecondary wake instability of a bridge model and its application in wake controlComputers & Fluids, 160, pp. 108–119, 2018. doi 10.1016/j.compfluid.2017.10.025
@article{2018:xin.zhang.ea:secondary, author = {Xin, Dabo and Zhang, Hongfu and Ou, Jinping}, title = {Secondary wake instability of a bridge model and its application in wake control}, journal = {Computers \& Fluids}, year = {2018}, volume = {160}, pages = {108--119}, publisher = {Elsevier}, doi = {10.1016/j.compfluid.2017.10.025}, groups = {app} }Three-dimensional spanwise-varying control, which is known to be related to secondary wake instability, has recently been reported as a highly efficient method to control vortex shedding. With the aim of suppressing Karman vortex shedding and the underlying aerodynamic forces in a bridge model using three-dimensional spanwise-varying control, Floquet stability analysis was applied to determine the most unstable secondary instability of a period vortex shedding wake at low Reynolds numbers (i.e. Re = 516, 774, and 1032). The numerical results showed that there was only a single peak of Floquet multipliers ranging from 1H to 6H, with H being the height of the bridge model; additionally, all Floquet modes were found to be analogous to the Mode-A type. Subsequently, spanwise-varying passive vortex generators (PVGs), which can trigger secondary instability of a wake by activating pairs of streamwise counter-rotating vortical structures, were applied to implement wake control. Large eddy simulation was used to verify the wake control effects with PVGs arranged on the lower surface of the bridge model. The results showed that, overall, the case of λ/H = 2 yields improved control effects on the fluctuating aerodynamic forces (an approximately 60% reduction in fluctuating lift and moment, 10% reduction in fluctuating drag). In addition, the PVG could effectively trigger and enhance the Mode-A-like flow pattern and suppress spanwise vortices. - W. He, P. Yu and L. K. B. LiBiBTeX AbstractGround effects on the stability of separated flow around a NACA 4415 airfoil at low Reynolds numbersAerospace Science and Technology, 72, pp. 63–76, 2018. doi 10.1016/j.ast.2017.10.039
@article{2018:he.yu.ea:ground, author = {He, Wei and Yu, Peng and Li, Larry KB}, title = {Ground effects on the stability of separated flow around a NACA 4415 airfoil at low Reynolds numbers}, journal = {Aerospace Science and Technology}, year = {2018}, volume = {72}, pages = {63--76}, publisher = {Elsevier}, doi = {10.1016/j.ast.2017.10.039}, groups = {app} }We perform a linear BiGlobal modal stability analysis on the separated flow around a NACA 4415 airfoil at low Reynolds numbers (300\-1000) and a high angle of attack (α=20), with a focus on the effect of the airfoil’s proximity to two different types of ground: a stationary ground and a moving ground. The results show that the most dominant perturbation is a Kelvin Helmholtz mode, which gives rise to a supercritical Hopf bifurcation to a global mode, leading to large-scale vortex shedding at a periodic limit cycle. As the airfoil approaches the ground, this mode can become more unstable or less unstable, depending on the specific type of ground: introducing a stationary ground to an otherwise groundless system is destabilizing but introducing a moving ground is stabilizing, although both effects weaken with increasing Re. By performing a Floquet analysis, we find that short-wavelength secondary instabilities are damped by a moving ground but are amplified by a stationary ground. By contrast, long-wavelength secondary instabilities are relatively insensitive to ground type. This numerical theoretical study shows that the ground can have an elaborate influence on the primary and secondary instabilities of the separated flow around an airfoil at low Re. These findings could be useful for the design of micro aerial vehicles and for improving our understanding of natural flyers such as insects and birds. - D. de Grazia, D. Moxey, S. J. Sherwin, M. A. Kravtsova and A. I. RubanBiBTeX AbstractDNS of a compressible boundary layer flow past an isolated three-dimensional hump in a high-speed subsonic regimePhysical Review Fluids, 3, p. 024101, 2018. doi 10.1103/PhysRevFluids.3.024101
@article{2018:grazia.moxey.ea:dns, author = {de Grazia, D. and Moxey, D. and Sherwin, S. J. and Kravtsova, M. A. and Ruban, A. I.}, title = {DNS of a compressible boundary layer flow past an isolated three-dimensional hump in a high-speed subsonic regime}, journal = {Physical Review Fluids}, year = {2018}, volume = {3}, pages = {024101}, doi = {10.1103/PhysRevFluids.3.024101}, groups = {app} }In this paper we study the boundary-layer separation produced in a high-speed subsonic boundary layer by a small wall roughness. Specifically, we present a direct numerical simulation (DNS) of a two-dimensional boundary-layer flow over a flat plate encountering a three-dimensional Gaussian-shaped hump. This work was motivated by the lack of DNS data of boundary-layer flows past roughness elements in a similar regime which is typical of civil aviation. The Mach and Reynolds numbers are chosen to be relevant for aeronautical applications when considering small imperfections at the leading edge of wings. We analyze different heights of the hump: The smaller heights result in a weakly nonlinear regime, while the larger result in a fully nonlinear regime with an increasing laminar separation bubble arising downstream of the roughness element and the formation of a pair of streamwise counterrotating vortices which appear to support themselves.
2017
- N. Yadav, S. W. Gepner and J. SzumbarskiBiBTeXInstability in a channel with grooves parallel to the flowPhysics of Fluids, 29 (8), p. 084104, 2017. doi 10.1063/1.4997950
@article{2017:yadav.gepner.ea:instability, author = {Yadav, Nikesh and Gepner, SW and Szumbarski, Jacek}, title = {Instability in a channel with grooves parallel to the flow}, journal = {Physics of Fluids}, year = {2017}, volume = {29}, number = {8}, pages = {084104}, doi = {10.1063/1.4997950}, publisher = {AIP Publishing}, groups = {app} } - F. Tong, L. Cheng, C. Xiong, S. Draper, H. An and X. LouBiBTeXFlow regimes for a square cross-section cylinder in oscillatory flowJournal of Fluid Mechanics, 813, pp. 85–109, 2017. doi 10.1017/jfm.2016.829
@article{2017:tong.cheng.ea:flow, author = {Tong, Feifei and Cheng, Liang and Xiong, Chengwang and Draper, Scott and An, Hongwei and Lou, Xiaofan}, title = {Flow regimes for a square cross-section cylinder in oscillatory flow}, journal = {Journal of Fluid Mechanics}, year = {2017}, volume = {813}, pages = {85--109}, doi = {10.1017/jfm.2016.829}, publisher = {Cambridge University Press}, groups = {app} } - G. Tang, L. Cheng, F. Tong, L. Lu and M. ZhaoBiBTeXModes of synchronisation in the wake of a streamwise oscillatory cylinderJournal of Fluid Mechanics, 832, pp. 146–169, 2017. doi 10.1017/jfm.2017.655
@article{2017:tang.cheng.ea:modes, author = {Tang, Guoqiang and Cheng, Liang and Tong, Feifei and Lu, Lin and Zhao, Ming}, title = {Modes of synchronisation in the wake of a streamwise oscillatory cylinder}, journal = {Journal of Fluid Mechanics}, year = {2017}, volume = {832}, pages = {146--169}, doi = {10.1017/jfm.2017.655}, publisher = {Cambridge University Press}, groups = {app} } - A. V. Proskurin and A. M. SagalakovBiBTeXA spectral/hp element solver for magnetohydrodynamicsarXiv preprint arXiv:1707.08957, 2017. doi 10.48550/arXiv.1707.08957
@article{2017:proskurin.sagalakov:spectralhp, author = {Proskurin, Alexander V and Sagalakov, Anatoly M}, title = {A spectral/hp element solver for magnetohydrodynamics}, journal = {arXiv preprint arXiv:1707.08957}, year = {2017}, doi = {10.48550/arXiv.1707.08957}, groups = {app} } - D. Moxey, C. D. Cantwell, G. Mengaldo, D. Serson, D. Ekelschot, J. Peiró, S. J. Sherwin and R. M. KirbyBiBTeX AbstractTowards p-adaptive spectral/hp element methods for modelling industrial flowsin Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, 2017, pp. 63–79. doi 10.1007/978-3-319-65870-4_4
@inproceedings{2017:moxey.cantwell.ea:towards*1, author = {Moxey, D. and Cantwell, C. D. and Mengaldo, G. and Serson, D. and Ekelschot, D. and Peir\'o, J. and Sherwin, S. J. and Kirby, R. M.}, title = {Towards $p$-adaptive spectral/$hp$ element methods for modelling industrial flows}, booktitle = {Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016}, year = {2017}, pages = {63--79}, doi = {10.1007/978-3-319-65870-4_4}, groups = {app} }There is an increasing requirement from both academia and industry for high-fidelity flow simulations that are able to accurately capture complicated and transient flow dynamics in complex geometries. Coupled with the growing availability of high-performance, highly parallel computing resources, there is therefore a demand for scalable numerical methods and corresponding software frameworks which can deliver the next-generation of complex and detailed fluid simulations to scientists and engineers in an efficient way. In this article we discuss recent and upcoming advances in the use of the \emphspectral/hp element method for addressing these modelling challenges. To use these methods efficiently for such applications, is critical that computational resolution is placed in the regions of the flow where it is needed most, which is often not known \empha priori. We propose the use of spatially and temporally varying polynomial order, coupled with appropriate error estimators, as key requirements in permitting these methods to achieve computationally efficient high-fidelity solutions to complex flow problems in the fluid dynamics community. - S. Ma, C.-W. Kang, T.-B. A. Lim, C.-H. Wu and O. TuttyBiBTeX AbstractWake of two side-by-side square cylinders at low Reynolds numbersPhysics of Fluids, 29 (3), p. 033604, 2017. doi 10.1063/1.4979134
@article{2017:ma.kang.ea:wake, author = {Ma, Shengwei and Kang, Chang-Wei and Lim, Teck-Bin Arthur and Wu, Chih-Hua and Tutty, Owen}, title = {Wake of two side-by-side square cylinders at low {Reynolds} numbers}, journal = {Physics of Fluids}, year = {2017}, volume = {29}, number = {3}, pages = {033604}, publisher = {AIP Publishing}, groups = {app}, doi = {10.1063/1.4979134} }Wake of two side-by-side square cylinders was investigated through direct numerical simulation at low Reynolds numbers (16-200). The gap between the two cylinders varied from 0 to 10D, where D is the dimension of the square cylinder (edge length). 9 different wake patterns and their dependency on both the Reynolds number and gap spacing were identified and analysed. A system classification map, demarcated by the Reynolds number and gap ratio g* (g/D, where g is the gap spacing between 2 cylinders), was derived for these 9 wake modes. Steady-state wake (mode I) was observed when the Reynolds number is lower than the critical Reynolds number, which depends on g*. For the gap ratio less than 0.7, only single vortex street was observed. The single vortex street wake can be either symmetric and periodic (mode II), or asymmetric and periodic (mode III), or irregular (mode IV). In this gap ratio range (less than 0.7), shedding frequency decreases with the gap ratio due to the damping role of the gap flow. For the gap ratio larger than 0.7, two vortex streets were also observed. For the gap ratio larger than 1, only two vortex streets were observed. Vortex shedding can be either synchronized and in-phase (mode V), synchronized and anti-phase (mode VI), in-phase dominated with low frequency modulation (mode VII), anti-phase dominated with low frequency modulation (mode VIII), asymmetric synchronized anti-phase (mode IX), or irregular (mode IV). For the gap ratio larger than 4, only synchronized anti-phase mode was observed under the conditions of this study. In the two vortex streets regime, shedding frequency is higher than that of a single cylinder, due to a stronger gap flow than that in the freestream side. The impact of gap ratio and Reynolds number on the drag and lift forces was also studied. - M. R. Jotkar and R. GovindarajanBiBTeXNon-modal stability of Jeffery-Hamel flowPhysics of Fluids, 29 (6), p. 064107, 2017. doi 10.1063/1.4983725
@article{2017:jotkar.govindarajan:non-modal, author = {Jotkar, Mamta R and Govindarajan, Rama}, title = {Non-modal stability of Jeffery-Hamel flow}, journal = {Physics of Fluids}, year = {2017}, volume = {29}, number = {6}, pages = {064107}, doi = {10.1063/1.4983725}, publisher = {AIP Publishing}, groups = {app} } - M. Hess and G. RozzaBiBTeXA Spectral Element Reduced Basis Method in Parametric CFDarXiv preprint arXiv:1712.06432, 2017. doi 10.48550/arXiv.1712.06432
@article{2017:hess.rozza:spectral, author = {Hess, Martin and Rozza, Gianluigi}, title = {A Spectral Element Reduced Basis Method in Parametric CFD}, journal = {arXiv preprint arXiv:1712.06432}, year = {2017}, doi = {10.48550/arXiv.1712.06432}, groups = {app} } - W. He, R. S. Gioria, J. M. Pérez and V. TheofilisBiBTeX AbstractLinear instability of low Reynolds number massively separated flow around three NACA airfoilsJournal of Fluid Mechanics, 811, pp. 701–741, 2017. doi 10.1017/jfm.2016.778
@article{2017:he.gioria.ea:linear, author = {He, W. and Gioria, R. S. and P\'erez, J. M. and Theofilis, V.}, title = {Linear instability of low {Reynolds} number massively separated flow around three {NACA} airfoils}, journal = {Journal of Fluid Mechanics}, year = {2017}, volume = {811}, pages = {701--741}, doi = {10.1017/jfm.2016.778}, publisher = {Cambridge University Press}, groups = {app} }Two- and three-dimensional modal and non-modal instability mechanisms of steady spanwise-homogeneous laminar separated flow over airfoil profiles, placed at large angles of attack against the oncoming flow, have been investigated using global linear stability theory. Three NACA profiles of distinct thickness and camber were considered in order to assess geometry effects on the laminar-turbulent transition paths discussed. At the conditions investigated, large-scale steady separation occurs, such that Tollmien-Schlichting and cross-flow mechanisms have not been considered. It has been found that the leading modal instability on all three airfoils is that associated with the Kelvin-Helmholtz mechanism, taking the form of the eigenmodes known from analysis of generic bluff bodies. The three-dimensional stationary eigenmode of the two-dimensional laminar separation bubble, associated in earlier analyses with the formation on the airfoil surface of large-scale separation patterns akin to stall cells, is shown to be more strongly damped than the Kelvin-Helmholtz mode at all conditions examined. Non-modal instability analysis reveals the potential of the flows considered to sustain transient growth which becomes stronger with increasing angle of attack and Reynolds number. Optimal initial conditions have been computed and found to be analogous to those on a cascade of low pressure turbine blades. By changing the time horizon of the analysis, these linear optimal initial conditions have been found to evolve into the Kelvin-Helmholtz mode. The time-periodic base flows ensuing linear amplification of the Kelvin-Helmholtz mode have been analysed via temporal Floquet theory. Two amplified modes have been discovered, having characteristic spanwise wavelengths of approximately 0.6 and 2 chord lengths, respectively. Unlike secondary instabilities on the circular cylinder, three-dimensional short-wavelength perturbations are the first to become linearly unstable on all airfoils. Long-wavelength perturbations are quasi-periodic, standing or travelling-wave perturbations that also become unstable as the Reynolds number is further increased. The dominant short-wavelength instability gives rise to spanwise periodic wall-shear patterns, akin to the separation cells encountered on airfoils at low angles of attack and the stall cells found in flight at conditions close to stall. Thickness and camber have quantitative but not qualitative effect on the secondary instability analysis results obtained. - L. M. Gonzalez, E. Ferrer and H. R. Diaz-OjedaBiBTeXOnset of three-dimensional flow instabilities in lid-driven circular cavitiesPhysics of Fluids, 29 (6), p. 064102, 2017. doi 10.1063/1.4984242
@article{2017:gonzalez.ferrer.ea:onset, author = {Gonzalez, LM and Ferrer, E and Diaz-Ojeda, HR}, title = {Onset of three-dimensional flow instabilities in lid-driven circular cavities}, journal = {Physics of Fluids}, year = {2017}, volume = {29}, number = {6}, pages = {064102}, doi = {10.1063/1.4984242}, publisher = {AIP Publishing}, groups = {app} } - S. ChunBiBTeX AbstractMethod of moving frames to solve time-dependent Maxwell’s equations on anisotropic curved surfaces: Applications to invisible cloak and ELF propagationJournal of Computational Physics, 340, pp. 85–104, 2017. doi 10.1016/j.jcp.2017.03.031
@article{2017:chun:method, author = {Chun, Sehun}, title = {Method of moving frames to solve time-dependent {Maxwell}'s equations on anisotropic curved surfaces: {Applications} to invisible cloak and {ELF} propagation}, journal = {Journal of Computational Physics}, year = {2017}, volume = {340}, pages = {85--104}, publisher = {Elsevier}, groups = {app}, doi = {10.1016/j.jcp.2017.03.031} }Applying the method of moving frames to Maxwell’s equations yields two important advancements for scientific computing. The first is the use of upwind flux for anisotropic materials in Maxwell’s equations, especially in the context of discontinuous Galerkin (DG) methods. Upwind flux has been available only to isotropic material, because of the difficulty of satisfying the Rankine-Hugoniot conditions in anisotropic media. The second is to solve numerically Maxwell’s equations on curved surfaces without the metric tensor and composite meshes. For numerical validation, spectral convergences are displayed for both two-dimensional anisotropic media and isotropic spheres. In the first application, invisible two-dimensional metamaterial cloaks are simulated with a relatively coarse mesh by both the lossless Drude model and the piecewisely-parametered layered model. In the second application, extremely low frequency propagation on various surfaces such as spheres, irregular surfaces, and non-convex surfaces is demonstrated. - S. Chun and C. EskilssonBiBTeX AbstractMethod of moving frames to solve the shallow water equations on arbitrary rotating curved surfacesJournal of Computational Physics, 333, pp. 1–23, 2017. doi 10.1016/j.jcp.2016.12.013
@article{2017:chun.eskilsson:method, author = {Chun, S and Eskilsson, Claes}, title = {Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces}, journal = {Journal of Computational Physics}, year = {2017}, volume = {333}, pages = {1--23}, publisher = {Elsevier}, groups = {app}, doi = {10.1016/j.jcp.2016.12.013} }A novel numerical scheme is proposed to solve the shallow water equations (SWEs) on arbitrary rotating curved surfaces. Based on the method of moving frames (MMF) in which the geometry is represented by orthonormal vectors, the proposed scheme not only has the fewest dimensionality both in space and time, but also does not require either of metric tensors, composite meshes, or the ambient space. The MMF-SWE formulation is numerically discretized using the discontinuous Galerkin method of arbitrary polynomial order p in space and an explicit Runge-Kutta scheme in time. The numerical model is validated against six standard tests on the sphere and the optimal order of convergence of is numerically demonstrated. The MMF-SWE scheme is also demonstrated for its efficiency and stability on the general rotating surfaces such as ellipsoid, irregular, and non-convex surfaces.
2016
- H. Xu, S. J. Sherwin, P. Hall and X. WuBiBTeXThe behaviour of Tollmien-Schlichting waves undergoing small-scale localised distortionsJOURNAL OF FLUID MECHANICS, 792, pp. 499–525, 2016. doi 10.1017/jfm.2016.93
@article{2016:xu.sherwin.ea:behaviour, author = {Xu, H and Sherwin, SJ and Hall, P and Wu, X}, title = {The behaviour of Tollmien-Schlichting waves undergoing small-scale localised distortions}, journal = {JOURNAL OF FLUID MECHANICS}, year = {2016}, volume = {792}, pages = {499--525}, month = apr, publisher = {CAMBRIDGE UNIV PRESS}, doi = {10.1017/jfm.2016.93}, issn = {0022-1120}, keyword = {TRANSITION}, language = {English}, day = {1}, publicationstatus = {published}, groups = {app} } - J.-E. W. Lombard, D. Moxey, S. J. Sherwin, J. F. A. Hoessler, S. Dhandapani and M. J. TaylorBiBTeXImplicit Large-Eddy Simulation of a Wingtip VortexAIAA JOURNAL, 54 (2), pp. 506–518, 2016. doi 10.2514/1.J054181
@article{2016:lombard.moxey.ea:implicit, author = {Lombard, J-EW and Moxey, D and Sherwin, SJ and Hoessler, JFA and Dhandapani, S and Taylor, MJ}, title = {Implicit Large-Eddy Simulation of a Wingtip Vortex}, journal = {AIAA JOURNAL}, year = {2016}, volume = {54}, pages = {506--518}, month = feb, publisher = {AMER INST AERONAUTICS ASTRONAUTICS}, doi = {10.2514/1.J054181}, issn = {0001-1452}, issue = {2}, keyword = {STABILIZATION}, language = {English}, day = {1}, publicationstatus = {published}, groups = {app} } - H. Jiang, L. Cheng, F. Tong, S. Draper and H. AnBiBTeXStable state of Mode A for flow past a circular cylinderPhysics of Fluids, 28 (10), p. 104103, 2016. doi 10.1063/1.4964379
@article{2016:jiang.cheng.ea:stable, author = {Jiang, Hongyi and Cheng, Liang and Tong, Feifei and Draper, Scott and An, Hongwei}, title = {Stable state of Mode A for flow past a circular cylinder}, journal = {Physics of Fluids}, year = {2016}, volume = {28}, number = {10}, pages = {104103}, doi = {10.1063/1.4964379}, publisher = {AIP Publishing}, groups = {app} } - S. W. Gepner and J. M. FloryanBiBTeXFlow dynamics and enhanced mixing in a converging–diverging channelJournal of Fluid Mechanics, 807, pp. 167–204, 2016. doi 10.1017/jfm.2016.621
@article{2016:gepner.floryan:flow, author = {Gepner, SW and Floryan, JM}, title = {Flow dynamics and enhanced mixing in a converging--diverging channel}, journal = {Journal of Fluid Mechanics}, year = {2016}, volume = {807}, pages = {167--204}, doi = {10.1017/jfm.2016.621}, publisher = {Cambridge University Press}, groups = {app} }
2015
- C. H. Roney, K. N. Tzortzis, C. D. Cantwell, N. A. Qureshi, R. L. Ali, P. B. Lim, J. H. Siggers, F. S. Ng and N. S. PetersBiBTeXA technique for visualising three-dimensional left atrial cardiac activation data in two dimensions with minimal distance distortionin Engineering in Medicine and Biology Society (EMBC), 2015 37th Annual International Conference of the IEEE, 2015, pp. 7296–7299. doi 10.1109/EMBC.2015.7320076
@inproceedings{2015:roney.tzortzis.ea:technique, author = {Roney, Caroline H and Tzortzis, Konstantinos N and Cantwell, Chris D and Qureshi, Norman A and Ali, Rheeda L and Lim, Phang Boon and Siggers, Jennifer H and Ng, Fu Siong and Peters, Nicholas S}, title = {A technique for visualising three-dimensional left atrial cardiac activation data in two dimensions with minimal distance distortion}, booktitle = {Engineering in Medicine and Biology Society (EMBC), 2015 37th Annual International Conference of the IEEE}, year = {2015}, pages = {7296--7299}, organization = {IEEE}, doi = {10.1109/EMBC.2015.7320076}, groups = {app} } - G. Rocco, T. A. Zaki, X. Mao, H. M. Blackburn and S. J. SherwinBiBTeXFloquet and transient growth stability analysis of a flow through a compressor passageAEROSPACE SCIENCE AND TECHNOLOGY, 44, pp. 116–124, 2015. doi 10.1016/j.ast.2015.02.004
@article{2015:rocco.zaki.ea:floquet, author = {Rocco, G. and Zaki, T. A. and Mao, X. and Blackburn, H. M. and Sherwin, S. J.}, title = {Floquet and transient growth stability analysis of a flow through a compressor passage}, journal = {AEROSPACE SCIENCE AND TECHNOLOGY}, year = {2015}, volume = {44}, pages = {116--124}, month = jul, publisher = {ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER}, doi = {10.1016/j.ast.2015.02.004}, issn = {1270-9638}, keyword = {WAKES}, language = {English}, day = {1}, publicationstatus = {published}, groups = {app} } - G. Rocco and S. J. SherwinBiBTeX AbstractThe role of spanwise forcing on vortex shedding suppression in a flow past a cylinderFluid Mechanics and its Applications, 107, pp. 105–110, 2015. doi 10.1007/978-3-319-06260-0_15
@article{2015:rocco.sherwin:role, author = {Rocco, G. and Sherwin, S. J.}, title = {The role of spanwise forcing on vortex shedding suppression in a flow past a cylinder}, journal = {Fluid Mechanics and its Applications}, year = {2015}, volume = {107}, pages = {105--110}, month = jan, doi = {10.1007/978-3-319-06260-0_15}, issn = {0926-5112}, day = {1}, publicationstatus = {published}, groups = {app} }Controlling the wake vortex dynamics of bluff bodies efficiently is a fundamental problem in many applications. Earlier direct numerical simulations (Darekar and Sherwin) of three-dimensional bluff bodies demonstrated that the introduction of a spanwise waviness at both the leading and trailing surfaces suppresses the vortex shedding and reduces the amplitude of the fluctuating aerodynamic forces. Under this motivation, starting from a fully developed shedding, a sufficiently high spanwise forcing is introduced on the surface of the cylinder, in the regions where separation effects occur, resulting in the stabilisation of the near wake in a timeindependent state, similar to the effect of a sinusoidal stagnation surface. Stability analysis of the linearised Navier-Stokes equations was then performed on the threedimensional flows to investigate the role of the spanwise modulation on the absolute instability associated with the von Karman street. - R. C. Moura, S. J. Sherwin and J. PeiroBiBTeXLinear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methodsJOURNAL OF COMPUTATIONAL PHYSICS, 298, pp. 695–710, 2015. doi 10.1016/j.jcp.2015.06.020
@article{2015:moura.sherwin.ea:linear, author = {Moura, R. C. and Sherwin, S. J. and Peiro, J.}, title = {Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods}, journal = {JOURNAL OF COMPUTATIONAL PHYSICS}, year = {2015}, volume = {298}, pages = {695--710}, month = oct, publisher = {ACADEMIC PRESS INC ELSEVIER SCIENCE}, doi = {10.1016/j.jcp.2015.06.020}, issn = {0021-9991}, keyword = {SCHEMES}, language = {English}, day = {1}, publicationstatus = {published}, groups = {app} } - M. Mirzargar, J. K. Ryan and R. M. KirbyBiBTeXSmoothness-Increasing Accuracy-Conserving (SIAC) Filtering and Quasi-Interpolation: A Unified ViewJournal of Scientific Computing, 2015. doi 10.1007/s10915-015-0081-9
@article{2015:mirzargar.ryan.ea:smoothness-increasing, author = {Mirzargar, Mahsa and Ryan, Jennifer K. and Kirby, Robert M.}, title = {Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering and Quasi-Interpolation: A Unified View}, journal = {Journal of Scientific Computing}, year = {2015}, doi = {10.1007/s10915-015-0081-9}, groups = {app} } - G. Mengaldo, M. Kravtsova, A. I. Ruban and S. J. SherwinBiBTeXTriple-deck and direct numerical simulation analyses of high-speed subsonic flows past a roughness elementJ. Fluid Mech., 774, pp. 311–323, 2015. doi 10.1017/jfm.2015.281
@article{2015:mengaldo.kravtsova.ea:triple-deck, author = {Mengaldo, G. and Kravtsova, M. and Ruban, A. I. and Sherwin, S. J.}, title = {Triple-deck and direct numerical simulation analyses of high-speed subsonic flows past a roughness element}, journal = {J. Fluid Mech.}, year = {2015}, volume = {774}, pages = {311--323}, month = jul, publisher = {CAMBRIDGE UNIV PRESS}, doi = {10.1017/jfm.2015.281}, issn = {0022-1120}, keyword = {CORNERS}, language = {English}, day = {1}, publicationstatus = {published}, groups = {app} } - X. Li, J. K. Ryan, R. M. Kirby and C. VuikBiBTeXSmoothness-Increasing Accuracy-Conserving (SIAC) Filters for Derivative Approximations of discontinuous Galerkin (DG) Solutions over Nonuniform Meshes and Near BoundariesJournal of Computational and Applied Mathematics, 2015. doi 10.1016/j.cam.2015.08.011
@article{2015:li.ryan.ea:smoothness-increasing, author = {Li, X. and Ryan, J. K. and Kirby, R. M. and Vuik, C.}, title = {Smoothness-Increasing Accuracy-Conserving (SIAC) Filters for Derivative Approximations of discontinuous Galerkin (DG) Solutions over Nonuniform Meshes and Near Boundaries}, journal = {Journal of Computational and Applied Mathematics}, year = {2015}, doi = {10.1016/j.cam.2015.08.011}, groups = {app} } - B. E. Jordi, C. J. Cotter and S. J. SherwinBiBTeXAn adaptive selective frequency damping methodPHYSICS OF FLUIDS, 27 (9), 2015. doi 10.1063/1.4932107
@article{2015:jordi.cotter.ea:adaptive, author = {Jordi, B. E. and Cotter, C. J. and Sherwin, S. J.}, title = {An adaptive selective frequency damping method}, journal = {PHYSICS OF FLUIDS}, year = {2015}, volume = {27}, number = {ARTN 094104}, month = sep, publisher = {AMER INST PHYSICS}, doi = {10.1063/1.4932107}, issn = {1070-6631}, issue = {9}, keyword = {FLOW}, language = {English}, day = {1}, publicationstatus = {published}, groups = {app} } - A. Comerford, K. Y. Chooi, M. Nowak, P. D. Weinberg and S. J. SherwinBiBTeXA combined numerical and experimental framework for determining permeability properties of the arterial mediaBIOMECHANICS AND MODELING IN MECHANOBIOLOGY, 14 (2), pp. 297–313, 2015. doi 10.1007/s10237-014-0604-6
@article{2015:comerford.chooi.ea:combined, author = {Comerford, A. and Chooi, K. Y. and Nowak, M. and Weinberg, P. D. and Sherwin, S. J.}, title = {A combined numerical and experimental framework for determining permeability properties of the arterial media}, journal = {BIOMECHANICS AND MODELING IN MECHANOBIOLOGY}, year = {2015}, volume = {14}, pages = {297--313}, month = apr, publisher = {SPRINGER HEIDELBERG}, doi = {10.1007/s10237-014-0604-6}, issn = {1617-7959}, issue = {2}, keyword = {ALBUMIN}, language = {English}, day = {1}, publicationstatus = {published}, groups = {app} } - S. Claus, C. D. Cantwell and T. N. PhillipsBiBTeXSpectral/hp element methods for plane Newtonian extrudate swellComputers & Fluids, 116, pp. 105–117, 2015. doi 10.48550/arXiv.1408.5167
@article{2015:claus.cantwell.ea:spectralhp, author = {Claus, Susanne and Cantwell, CD and Phillips, TN}, title = {Spectral/hp element methods for plane Newtonian extrudate swell}, journal = {Computers \& Fluids}, year = {2015}, volume = {116}, pages = {105--117}, doi = {10.48550/arXiv.1408.5167}, publisher = {Elsevier}, groups = {app} }
2014
- J. King, S. Yakovlev, Z. Fu, R. M. Kirby and S. J. SherwinBiBTeXExploiting Batch Processing on Streaming Architectures to Solve 2D Elliptic Finite Element Problems: A Hybridized Discontinuous Galerkin (HDG) Case StudyJOURNAL OF SCIENTIFIC COMPUTING, 60 (2), pp. 457–482, 2014. doi 10.1007/s10915-013-9805-x
@article{2014:king.yakovlev.ea:exploiting, author = {King, J. and Yakovlev, S. and Fu, Z. and Kirby, R. M. and Sherwin, S. J.}, title = {Exploiting Batch Processing on Streaming Architectures to Solve 2D Elliptic Finite Element Problems: A Hybridized Discontinuous Galerkin (HDG) Case Study}, journal = {JOURNAL OF SCIENTIFIC COMPUTING}, year = {2014}, volume = {60}, pages = {457--482}, month = aug, publisher = {SPRINGER/PLENUM PUBLISHERS}, doi = {10.1007/s10915-013-9805-x}, issn = {0885-7474}, issue = {2}, keyword = {Graphical processing units (GPUs)}, language = {English}, day = {1}, publicationstatus = {published}, groups = {app} }
2013
- S. Shastry and R. M. KirbyBiBTeX AbstractOn Interpolation Errors over Quadratic Nodal Triangular Finite Elementsin 22nd International Meshing Roundtable, Orlando, FL, 2013. doi 10.1007/978-3-319-02335-9_20
@inproceedings{2013:shastry.kirby:on, author = {Shastry, Shankar and Kirby, Robert M.}, title = {On Interpolation Errors over Quadratic Nodal Triangular Finite Elements}, year = {2013}, month = oct, journal = {22nd International Meshing Roundtable, Orlando, FL}, doi = {10.1007/978-3-319-02335-9_20}, groups = {app} }Interpolation techniques are used to estimate function values and their derivatives at those points for which a numerical solution of any equation is not explicitly evaluated. In particular, the shape functions are used to interpolate a solution (within an element) of a partial differential equation obtained by the finite element method. Mesh generation and quality improvement are often driven by the objective of minimizing the bounds on the error of the interpolated solution. For linear elements, the error bounds at a point have been derived as a composite function of the shape function values at the point and its distance from the elementś nodes. We extend the derivation to quadratic triangular elements and visualize the bounds for both the function interpolant and the interpolant of its derivative. The maximum error bound for a function interpolant within an element is computed using the active set method for constrained optimization. For the interpolant of the derivative, we visually observe that the evaluation of the bound at the corner vertices is sufficient to find the maximum bound within an element.We characterize the bounds and develop a mesh quality improvement algorithm that optimizes the bounds through the movement (r-refinement) of both the corner vertices and edge nodes in a high-order mesh. - V. Peiffer, S. J. Sherwin and P. D. WeinbergBiBTeX AbstractComputation in the rabbit aorta of a new metric - the transverse wall shear stress - to quantify the multidirectional character of disturbed blood flowJOURNAL OF BIOMECHANICS, 46 (15), pp. 2651–2658, 2013. doi 10.1016/j.jbiomech.2013.08.003
@article{2013:peiffer.sherwin.ea:computation, author = {Peiffer, V. and Sherwin, S. J. and Weinberg, P. D.}, title = {Computation in the rabbit aorta of a new metric - the transverse wall shear stress - to quantify the multidirectional character of disturbed blood flow}, journal = {JOURNAL OF BIOMECHANICS}, year = {2013}, volume = {46}, pages = {2651--2658}, month = oct, publisher = {ELSEVIER SCI LTD}, doi = {10.1016/j.jbiomech.2013.08.003}, issn = {0021-9290}, issue = {15}, keyword = {BRANCHES}, language = {English}, day = {18}, publicationstatus = {published}, groups = {app} }Spatial variation of the haemodynamic stresses acting on the arterial wall is commonly assumed to explain the focal development of atherosclerosis. Disturbed flow in particular is thought to play a key role. However, widely-used metrics developed to quantify its extent are unable to distinguish between uniaxial and multidirectional flows. We analysed pulsatile flow fields obtained in idealised and anatomically-realistic arterial geometries using computational fluid dynamics techniques, and in particular investigated the multidirectionality of the flow fields, capturing this aspect of near-wall blood flow with a new metric, the transverse wall shear stress (transWSS), calculated as the time-average of wall shear stress components perpendicular to the mean flow direction. In the idealised branching geometry, multidirectional flow was observed downstream of the branch ostium, a region of flow stagnation, and to the sides of the ostium. The distribution of the transWSS was different from the pattern of traditional haemodynamic metrics and more dependent on the velocity waveform imposed at the branch outlet. In rabbit aortas, transWSS patterns were again different from patterns of traditional metrics. The near-branch pattern varied between intercostal ostia, as is the case for lesion distribution; for some branches there were striking resemblances to the age-dependent patterns of disease seen in rabbit and human aortas. The new metric may lead to improved understanding of atherogenesis. - H. Mirzaee, J. King, J. K. Ryan and R. M. KirbyBiBTeX AbstractSmoothness-Increasing Accuracy-Conserving (SIAC) Filters for Discontinuous Galerkin Solutions Over Unstructured Triangular MeshesSIAM Journal of Scientific Computing, 35 (1), pp. 212–230, 2013. doi 10.1016/j.cam.2015.08.011
@article{2013:mirzaee.king.ea:smoothness-increasing, author = {Mirzaee, Hanieh and King, James and Ryan, Jennifer K. and Kirby, Robert M.}, title = {Smoothness-Increasing Accuracy-Conserving (SIAC) Filters for Discontinuous Galerkin Solutions Over Unstructured Triangular Meshes}, journal = {SIAM Journal of Scientific Computing}, year = {2013}, volume = {35}, number = {1}, pages = {212--230}, doi = {10.1016/j.cam.2015.08.011}, groups = {app} }Accurate approximations for the derivatives are usually required in many application areas such as biomechanics, chemistry and visualization applications. With the help of Smoothness-Increasing Accuracy-Conserving (SIAC) filtering, one can enhance the derivatives of a discontinuous Galerkin solution. However, current investigations of derivative filtering are limited to uniform meshes and periodic boundary conditions, which do not meet practical requirements. The purpose of this paper is twofold: to extend derivative filtering to nonuniform meshes and propose position-dependent derivative filters to handle filtering near the boundaries. Through analyzing the error estimates for SIAC filtering, we extend derivative filtering to nonuniform meshes by changing the scaling of the filter. For filtering near boundaries, we discuss the advantages and disadvantages of two existing position-dependent filters and then extend them to position-dependent derivative filters, respectively. Further, we prove that with the position-dependent derivative filters, the filtered solutions can obtain a better accuracy rate compared to the original discontinuous Galerkin approximation with arbitrary derivative orders over nonuniform meshes. One- and two-dimensional numerical results are provided to support the theoretical results and demonstrate that the position-dependent derivative filters, in general, enhance the accuracy of the solution for both uniform and nonuniform meshes. - J. King and R. M. KirbyBiBTeX AbstractA Scalable, Efficient Scheme for the Evaluation of Stencil Computations over Unstructured MeshesIEEE SuperComputing 2013, Denver, CO, 2013. doi 10.1145/2503210.2503214
@article{2013:king.kirby:scalable, author = {King, James and Kirby, Robert M.}, title = {A Scalable, Efficient Scheme for the Evaluation of Stencil Computations over Unstructured Meshes}, journal = {IEEE SuperComputing 2013, Denver, CO}, year = {2013}, month = nov, doi = {10.1145/2503210.2503214}, groups = {app} }Stencil computations are a common class of operations that appear in many computational scientific and engineering applications. Stencil computations often benefit from compiletime analysis, exploiting data-locality, and parallelism. Post-processing of discontinuous Galerkin (dG) simulation solutions with B-spline kernels is an example of a numerical method which requires evaluating computationally intensive stencil operations over a mesh. Previous work on stencil computations has focused on structured meshes, while giving little attention to unstructured meshes. Performing stencil operations over an unstructured mesh requires sampling of heterogeneous elements which often leads to inefficient memory access patterns and limits data locality/reuse. In this paper, we present an efficient method for performing stencil computations over unstructured meshes which increases data-locality and cache efficiency, and a scalable approach for stencil tiling and concurrent execution. We provide experimental results in the context of post-processing of dG solutions that demonstrate the effectiveness of our approach. - H. M. Blackburn, P. Hall and S. J. SherwinBiBTeXLower branch equilibria in Couette flow: the emergence of canonical states for arbitrary shear flowsJOURNAL OF FLUID MECHANICS, 726 (ARTN R2), 2013. doi 10.1017/jfm.2013.254
@article{2013:blackburn.hall.ea:lower, author = {Blackburn, H. M. and Hall, P. and Sherwin, S. J.}, title = {Lower branch equilibria in Couette flow: the emergence of canonical states for arbitrary shear flows}, journal = {JOURNAL OF FLUID MECHANICS}, year = {2013}, volume = {726}, number = {ARTN R2}, month = jul, publisher = {CAMBRIDGE UNIV PRESS}, doi = {10.1017/jfm.2013.254}, issn = {0022-1120}, keyword = {VORTICES}, language = {English}, day = {1}, publicationstatus = {published}, groups = {app} }
2012
- V. Peiffer, E. M. Rowland, S. G. Cremers, P. D. Weinberg and S. J. SherwinBiBTeX AbstractEffect of aortic taper on patterns of blood flow and wall shear stress in rabbits: Association with ageATHEROSCLEROSIS, 223 (1), pp. 114–121, 2012. doi 10.1016/j.atherosclerosis.2012.04.020
@article{2012:peiffer.rowland.ea:effect, author = {Peiffer, V. and Rowland, E. M. and Cremers, S. G. and Weinberg, P. D. and Sherwin, S. J.}, title = {Effect of aortic taper on patterns of blood flow and wall shear stress in rabbits: Association with age}, journal = {ATHEROSCLEROSIS}, year = {2012}, volume = {223}, pages = {114--121}, month = jul, publisher = {ELSEVIER IRELAND LTD}, doi = {10.1016/j.atherosclerosis.2012.04.020}, issn = {0021-9150}, issue = {1}, keyword = {ARCH}, language = {English}, day = {1}, publicationstatus = {published}, groups = {app} }Objective: The distribution of atherosclerotic lesions changes with age in human and rabbit aortas. We investigated if this can be explained by changes in patterns of blood flow and wall shear stress. Methods: The luminal geometry of thoracic aortas from immature and mature rabbits was obtained by micro-CT of vascular corrosion casts. Blood flow was computed and average maps of wall shear stress were derived. Results: The branch anatomy of the aortic arch varied widely between animals. Wall shear was increased downstream and to a lesser extent upstream of intercostal branch ostia, and a stripe of high shear was located on the dorsal descending aortic wall. The stripe was associated with two vortices generated by aortic arch curvature; their persistence into the descending aorta depended on aortic taper and was more pronounced in mature geometries. These results were not sensitive to the modelling assumptions. Conclusions: Blood flow characteristics in the rabbit aorta were affected by the degree of taper, which tends to increase with age in the aortic arch and strengthens secondary flows into the descending aorta. Previously-observed lesion distributions correlated better with high than low shear, and age-related changes around branch ostia were not explained by the flow patterns. - B. Nelson, E. Liu, R. Haimes and R. M. KirbyBiBTeXElVis: A System for the Accurate and Interactive Visualization of High-Order Finite Element SolutionsIEEE Transactions on Visualization and Computer Graphics (IEEE Visualization Issue), 18 (12), pp. 2325–2334, 2012. doi 10.1109/TVCG.2012.218
@article{2012:nelson.liu.ea:elvis, author = {Nelson, Blake and Liu, Eric and Haimes, Robert and Kirby, Robert M.}, title = {ElVis: A System for the Accurate and Interactive Visualization of High-Order Finite Element Solutions}, journal = {IEEE Transactions on Visualization and Computer Graphics (IEEE Visualization Issue)}, year = {2012}, volume = {18}, number = {12}, pages = {2325--2334}, doi = {10.1109/TVCG.2012.218}, groups = {app} } - H. Mirzaee, J. K. Ryan and R. M. KirbyBiBTeX AbstractEfficient Implementation of Smoothness-Increasing Accuracy-Conserving (SIAC) Filters for Discontinuous Galerkin SolutionsJournal of Scientific Computing, 52 (1), pp. 85–112, 2012. doi 10.1007/s10915-011-9535-x
@article{2012:mirzaee.ryan.ea:efficient, author = {Mirzaee, Hanieh and Ryan, Jennifer K. and Kirby, Robert M.}, title = {Efficient Implementation of Smoothness-Increasing Accuracy-Conserving (SIAC) Filters for Discontinuous Galerkin Solutions}, journal = {Journal of Scientific Computing}, year = {2012}, volume = {52}, number = {1}, pages = {85--112}, doi = {10.1007/s10915-011-9535-x}, groups = {app} }The discontinuous Galerkin (DG) methods provide a high-order extension of the finite volume method in much the same way as high-order or spectral/hp elements extend standard finite elements. However, lack of inter-element continuity is often contrary to the smoothness assumptions upon which many post-processing algorithms such as those used in visualization are based. Smoothness-increasing accuracy-conserving (SIAC) filters were proposed as a means of ameliorating the challenges introduced by the lack of regularity at element interfaces by eliminating the discontinuity between elements in a way that is consistent with the DG methodology; in particular, high-order accuracy is preserved and in many cases increased. The goal of this paper is to explicitly define the steps to efficient computation of this filtering technique as applied to both structured triangular and quadrilateral meshes. Furthermore, as the SIAC filter is a good candidate for parallelization, we provide, for the first time, results that confirm anticipated performance scaling when parallelized on a shared-memory multi-processor machine. - J. King, H. Mirzaee, J. K. Ryan and R. M. KirbyBiBTeX AbstractSmoothness-Increasing Accuracy-Conserving (SIAC) Filtering for discontinuous Galerkin Solutions: Improved Errors Versus Higher-Order AccuracyJournal of Scientific Computing, 53 (1), pp. 129–149, 2012. doi 10.1016/j.cam.2015.08.011
@article{2012:king.mirzaee.ea:smoothness-increasing, author = {King, James and Mirzaee, Hanieh and Ryan, Jennifer K. and Kirby, Robert M.}, title = {Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for discontinuous Galerkin Solutions: Improved Errors Versus Higher-Order Accuracy}, journal = {Journal of Scientific Computing}, year = {2012}, volume = {53}, pages = {129--149}, issue = {1}, doi = {10.1016/j.cam.2015.08.011}, groups = {app} }Accurate approximations for the derivatives are usually required in many application areas such as biomechanics, chemistry and visualization applications. With the help of Smoothness-Increasing Accuracy-Conserving (SIAC) filtering, one can enhance the derivatives of a discontinuous Galerkin solution. However, current investigations of derivative filtering are limited to uniform meshes and periodic boundary conditions, which do not meet practical requirements. The purpose of this paper is twofold: to extend derivative filtering to nonuniform meshes and propose position-dependent derivative filters to handle filtering near the boundaries. Through analyzing the error estimates for SIAC filtering, we extend derivative filtering to nonuniform meshes by changing the scaling of the filter. For filtering near boundaries, we discuss the advantages and disadvantages of two existing position-dependent filters and then extend them to position-dependent derivative filters, respectively. Further, we prove that with the position-dependent derivative filters, the filtered solutions can obtain a better accuracy rate compared to the original discontinuous Galerkin approximation with arbitrary derivative orders over nonuniform meshes. One- and two-dimensional numerical results are provided to support the theoretical results and demonstrate that the position-dependent derivative filters, in general, enhance the accuracy of the solution for both uniform and nonuniform meshes. - J. Alastruey, K. H. Parker and S. J. Sherwinin BHR Group - 11th International Conferences on Pressure Surges, 2012, pp. 401–442.BiBTeX Abstract
@inproceedings{2012:alastruey.parker.ea:arterial, author = {Alastruey, J. and Parker, K. H. and Sherwin, S. J.}, title = {Arterial pulse wave haemodynamics}, booktitle = {BHR Group - 11th International Conferences on Pressure Surges}, year = {2012}, pages = {401--442}, month = dec, url = {https://kclpure.kcl.ac.uk/portal/en/publications/arterial-pulse-wave-haemodynamics}, isbn = {9781855981331}, day = {1}, publicationstatus = {published}, groups = {app} }The shape of the arterial pulse wave is intimately related to the physical properties of the cardiovascular system. Understanding the mechanisms underlying this relation is clinically relevant, since pulse waveforms carry valuable information for the diagnosis and treatment of disease. We overview some numerical, theoretical and experimental efforts (using in vivo and in vitro data) made in this field of research, focusing on the physical aspects of arterial pulse wave propagation in the systemic circulation. The mathematical and numerical tools that we describe are based on the one-dimensional formulation in the time-domain.
2011
- B. Nelson, R. Haimes and R. M. KirbyBiBTeX AbstractGPU-Based Interactive Cut-Surface Extraction From High-Order Finite Element FieldsIEEE Transactions on Visualization and Computer Graphics (IEEE Visualization Issue), 17 (12), pp. 1803–1811, 2011. doi 10.1109/TVCG.2011.206
@article{2011:nelson.haimes.ea:gpu-based, author = {Nelson, Blake and Haimes, Robert and Kirby, Robert M.}, title = {GPU-Based Interactive Cut-Surface Extraction From High-Order Finite Element Fields}, journal = {IEEE Transactions on Visualization and Computer Graphics (IEEE Visualization Issue)}, year = {2011}, volume = {17}, number = {12}, pages = {1803--1811}, doi = {10.1109/TVCG.2011.206}, groups = {app} }We present a GPU-based ray-tracing system for the accurate and interactive visualization of cut-surfaces through 3D simulations of physical processes created from spectral/hp high-order finite element methods. When used by the numerical analyst to debug the solver, the ability for the imagery to precisely reflect the data is critical. In practice, the investigator interactively selects from a palette of visualization tools to construct a scene that can answer a query of the data. This is effective as long as the implicit contract of image quality between the individual and the visualization system is upheld. OpenGL rendering of scientific visualizations has worked remarkably well for exploratory visualization for most solver results. This is due to the consistency between the use of first-order representations in the simulation and the linear assumptions inherent in OpenGL (planar fragments and color-space interpolation). Unfortunately, the contract is broken when the solver discretization is of higher-order. There have been attempts to mitigate this through the use of spatial adaptation and/or texture mapping. These methods do a better job of approximating what the imagery should be but are not exact and tend to be view-dependent. This paper introduces new rendering mechanisms that specifically deal with the kinds of native data generated by high-order finite element solvers. The exploratory visualization tools are reassessed and cast in this system with the focus on image accuracy. This is accomplished in a GPU setting to ensure interactivity. - H. Mirzaee, L. Yue, J. K. Ryan and R. M. KirbyBiBTeX AbstractSmoothness-Increasing Accuracy-Conserving (SIAC) Postprocessing for Discontinuous Galerkin Solutions Over Structured Triangular MeshesSIAM Journal of Numerical Analysis, 49 (5), pp. 1899–1920, 2011. doi 10.1137/110830678
@article{2011:mirzaee.yue.ea:smoothness-increasing, author = {Mirzaee, Hanieh and Yue, Liang and Ryan, Jennifer K. and Kirby, Robert M.}, title = {Smoothness-Increasing Accuracy-Conserving (SIAC) Postprocessing for Discontinuous Galerkin Solutions Over Structured Triangular Meshes}, journal = {SIAM Journal of Numerical Analysis}, year = {2011}, volume = {49}, number = {5}, pages = {1899--1920}, doi = {10.1137/110830678}, groups = {app} }Theoretically and computationally, it is possible to demonstrate that the order of accuracy of a discontinuous Galerkin (DG) solution for linear hyperbolic equations can be improved from order k+1 to 2k+1 through the use of smoothness-increasing accuracy-conserving (SIAC) filtering. However, it is a computationally complex task to perform this in an efficient manner, which becomes an even greater issue considering nonquadrilateral mesh structures. In this paper, we present an extension of this SIAC filter to structured triangular meshes. The basic theoretical assumption in the previous implementations of the postprocessor limits the use to numerical solutions solved over a quadrilateral mesh. However, this assumption is restrictive, which in turn complicates the application of this postprocessing technique to general tessellations. Additionally, moving from quadrilateral meshes to triangulated ones introduces more complexity in the calculations as the number of integrations required increases. In this paper, we extend the current theoretical results to variable coefficient hyperbolic equations over structured triangular meshes and demonstrate the effectiveness of the application of this postprocessor to structured triangular meshes as well as exploring the effect of using inexact quadrature. We show that there is a direct theoretical extension to structured triangular meshes for hyperbolic equations with bounded variable coefficients. This is a challenging first step toward implementing SIAC filters for unstructured tessellations. We show that by using the usual B-spline implementation, we are able to improve on the order of accuracy as well as decrease the magnitude of the errors. These results are valid regardless of whether exact or inexact integration is used. The results here demonstrate that it is still possible, both theoretically and computationally, to improve to 2k+1 over the DG solution itself for structured triangular meshes.
2010
- H. Mirzaee, J. K. Ryan and R. M. KirbyBiBTeX AbstractQuantification of Errors Introduced in the Numerical Approximation and Implementation of Smoothness-Increasing Accuracy Conserving (SIAC) Filtering of Discontinuous Galerkin (DG) FieldsJournal of Scientific Computing, 45, pp. 447–470, 2010. doi 10.1007/s10915-009-9342-9
@article{2010:mirzaee.ryan.ea:quantification, author = {Mirzaee, Hanieh and Ryan, Jennifer K. and Kirby, Robert M.}, title = {Quantification of Errors Introduced in the Numerical Approximation and Implementation of Smoothness-Increasing Accuracy Conserving (SIAC) Filtering of Discontinuous Galerkin (DG) Fields}, journal = {Journal of Scientific Computing}, year = {2010}, volume = {45}, pages = {447--470}, doi = {10.1007/s10915-009-9342-9}, groups = {app} }The discontinuous Galerkin (DG) method continues to maintain heightened levels of interest within the simulation community because of the discretization flexibility it provides. Although one of the fundamental properties of the DG methodology and arguably its most powerful property is the ability to combine high-order discretizations on an inter-element level while allowing discontinuities between elements, this flexibility generates a plethora of difficulties when one attempts to post-process DG fields for analysis and evaluation of scientific results. Smoothness-increasing accuracy-conserving (SIAC) filtering enhances the smoothness of the field by eliminating the discontinuity between elements in a way that is consistent with the DG methodology; in particular, high-order accuracy is preserved and in many cases increased. Fundamental to the post-processing approach is the convolution of a spline-based kernel against a DG field. This paper presents a study of the impact of numerical quadrature approximations on the resulting convolution. We discuss both theoretical estimates as well as empirical results which demonstrate the efficacy of the post-processing approach when different levels and types of quadrature approximation are used. Finally, we provide some guidelines for effective use of SIAC filtering of DG fields when used as input to common post-processing and visualization techniques. - P. Hall and S. SherwinBiBTeX AbstractStreamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structuresJOURNAL OF FLUID MECHANICS, 661, pp. 178–205, 2010. doi 10.1017/S0022112010002892
@article{2010:hall.sherwin:streamwise, author = {Hall, P. and Sherwin, S.}, title = {Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures}, journal = {JOURNAL OF FLUID MECHANICS}, year = {2010}, volume = {661}, pages = {178--205}, month = oct, publisher = {CAMBRIDGE UNIV PRESS}, doi = {10.1017/S0022112010002892}, issn = {0022-1120}, keyword = {STOKES EQUATIONS}, language = {English}, day = {25}, publicationstatus = {published}, groups = {app} }The relationship between asymptotic descriptions of vortex wave interactions and more recent work on exact coherent structures is investigated. In recent years immense interest has been focused on so-called self-sustained processes in turbulent shear flows where the importance of waves interacting with streamwise vortex flows has been elucidated in a number of papers. In this paper, it is shown that the so-called lower branch state which has been shown to play a crucial role in these self-sustained processes is a finite Reynolds number analogue of a Rayleigh vortex wave interaction with scales appropriately modified from those for external flows to Couette flow, the flow of interest here. Remarkable agreement between the asymptotic theory and numerical solutions of the Navier Stokes equations is found even down to relatively small Reynolds numbers, thereby suggesting the possible importance of vortex wave interaction theory in turbulent shear flows. The relevance of the work to more general shear flows is also discussed.
2009
- D. Walfisch, J. K. Ryan, R. M. Kirby and R. HaimesBiBTeX AbstractOne-Sided Smoothness-Increasing Accuracy-Conserving Filtering for Enhanced Streamline Integration through Discontinuous FieldsJournal of Scientific Computing , 38 (2), pp. 164–184, 2009. doi 10.1007/s10915-008-9230-8
@article{2009:walfisch.ryan.ea:one-sided, author = {Walfisch, David and Ryan, Jennifer K. and Kirby, Robert M. and Haimes, Robert}, title = {One-Sided Smoothness-Increasing Accuracy-Conserving Filtering for Enhanced Streamline Integration through Discontinuous Fields}, journal = {Journal of Scientific Computing }, year = {2009}, volume = {38}, number = {2}, pages = {164--184}, doi = {10.1007/s10915-008-9230-8}, groups = {app} }The discontinuous Galerkin (DG) method continues to maintain heightened levels of interest within the simulation community because of the discretization flexibility it provides. One of the fundamental properties of the DG methodology and arguably its most powerful property is the ability to combine high-order discretizations on an inter-element level while allowing discontinuities between elements. This flexibility, however, generates a plethora of difficulties when one attempts to use DG fields for feature extraction and visualization, as most post-processing schemes are not designed for handling explicitly discontinuous fields. This work introduces a new method of applying smoothness-increasing, accuracy-conserving filtering on discontinuous Galerkin vector fields for the purpose of enhancing streamline integration. The filtering discussed in this paper enhances the smoothness of the field and eliminates the discontinuity between elements, thus resulting in more accurate streamlines. Furthermore, as a means of minimizing the computational cost of the method, the filtering is done in a one-dimensional manner along the streamline.
2007
- M. Meyer, B. Nelson, R. M. Kirby and R. WhitakerBiBTeX AbstractParticle Systems for Efficient and Accurate Finite Element VisualizationIEEE Transactions on Visualization and Computer Graphics, 13 (5), pp. 1015–1026, 2007. doi 10.1109/TVCG.2007.1048
@article{2007:meyer.nelson.ea:particle, author = {Meyer, Miriah and Nelson, Blake and Kirby, Robert M. and Whitaker, Ross}, title = {Particle Systems for Efficient and Accurate Finite Element Visualization}, journal = {IEEE Transactions on Visualization and Computer Graphics}, year = {2007}, volume = {13}, number = {5}, pages = {1015--1026}, doi = {10.1109/TVCG.2007.1048}, groups = {app} }Visualization has become an important component of the simulation pipeline, providing scientists and engineers a visual intuition of their models. Simulations that make use of the high-order finite element method for spatial subdivision, however, present a challenge to conventional isosurface visualization techniques. High-order finite element isosurfaces are often defined by basis functions in reference space, which give rise to a world-space solution through a coordinate transformation, which does not necessarily have a closed-form inverse. Therefore, world-space isosurface rendering methods such as marching cubes and ray tracing must perform a nested root finding, which is computationally expensive. We thus propose visualizing these isosurfaces with a particle system. We present a framework that allows particles to sample an isosurface in reference space, avoiding the costly inverse mapping of positions from world space when evaluating the basis functions. The distribution of particles across the reference space isosurface is controlled by geometric information from the world-space isosurface such as the surface gradient and curvature. The resulting particle distributions can be distributed evenly or adapted to accommodate world-space surface features. This provides compact, efficient, and accurate isosurface representations of these challenging data sets. - S. Curtis, R. M. Kirby, J. K. Ryan and C.-W. ShuBiBTeX AbstractPost-processing for the Discontinuous Galerkin Method Over Non-Uniform MeshesSIAM Journal of Scientific Computing, 30 (1), pp. 272–289, 2007. doi 10.1137/070681284
@article{2007:curtis.kirby.ea:post-processing, author = {Curtis, Sean and Kirby, Robert M. and Ryan, Jennifer K. and Shu, Chi-Wang}, title = {Post-processing for the Discontinuous Galerkin Method Over Non-Uniform Meshes}, journal = {SIAM Journal of Scientific Computing}, year = {2007}, volume = {30}, number = {1}, pages = {272--289}, doi = {10.1137/070681284}, groups = {app} }A postprocessing technique based on negative order norm estimates for the discontinuous Galerkin methods was previously introduced by Cockburn, Luskin, Shu, and Suli [Proceedings of the International Symposium on Discontinuous Galerkin Methods, Springer, New York, pp. 291; Math. Comput., 72 (2003), pp. 577]. The postprocessor allows improvement in accuracy of the discontinuous Galerkin method for time-dependent linear hyperbolic equations from order k+1 to order 2k+1 over a uniform mesh. Assumptions on the convolution kernel along with uniformity in mesh size give a local translation invariant postprocessor that allows for simple implementation using small matrix-vector multiplications. In this paper, we present two alternatives for extending this postprocessing technique to include smoothly varying meshes. The first method uses a simple local L2-projection of the smoothly varying mesh to a locally uniform mesh and uses this projected solution to compute the postprocessed solution. By using this local L2-projection, recalculating the convolution kernel for every element can be avoided, and 2k+1 order accuracy of the postprocessed solution can be achieved. The second method uses the idea of characteristic length based upon the largest element size for the scaling of the postprocessing kernel. These two methods, local projection and characteristic length, are also applied to approximations over a mesh with elements that vary in size randomly. We discuss the computational issues in using these two techniques and demonstrate numerically that we obtain the 2k+1 order of accuracy for the smoothly varying meshes, and that although the 2k+1 order of accuracy is not fully realized for random meshes, there is significant improvement in the L2 errors.
2006
- B. Nelson and R. M. KirbyBiBTeX AbstractRay-Tracing Polymorphic Multi-Domain Spectral/hp Elements for Isosurface RenderingIEEE Transactions on Visualization and Computer Graphics, 12 (1), pp. 114–125, 2006. doi 10.1109/TVCG.2006.12
@article{2006:nelson.kirby:ray-tracing, author = {Nelson, Blake and Kirby, Robert M.}, title = {Ray-Tracing Polymorphic Multi-Domain Spectral/hp Elements for Isosurface Rendering}, journal = { IEEE Transactions on Visualization and Computer Graphics}, year = {2006}, volume = {12}, number = {1}, pages = {114--125}, doi = {10.1109/TVCG.2006.12}, groups = {app} }The purpose of this paper is to present a ray-tracing isosurface rendering algorithm for spectral/hp (high-order finite) element methods in which the visualization error is both quantified and minimized. Determination of the ray-isosurface intersection is accomplished by classic polynomial root-finding applied to a polynomial approximation obtained by projecting the finite element solution over element-partitioned segments along the ray. Combining the smoothness properties of spectral/hp elements with classic orthogonal polynomial approximation theory, we devise an adaptive scheme which allows the polynomial approximation along a ray-segment to be arbitrarily close to the true solution. The resulting images converge toward a pixel-exact image at a rate far faster than sampling the spectral/hp element solution and applying classic low-order visualization techniques such as marching cubes.
PhD theses
2025
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@phdthesis{2025:wustenberg:implicit, author = {Wustenberg, Henrik}, title = {Implicit time-stepping for scale-resolved industrial flow simulations using spectral/HP elements}, school = {Imperial College London}, year = {2025}, url = {https://hdl.handle.net/10044/1/121265}, doi = {10.25560/121265}, groups = {thesis} }Accurate numerical simulations of unsteady fluid flows require scale-resolving simulations which are, however, limited in applications due to high computational costs. Since computational resources are limited, cost and time constraints require algorithmic improvements instead. Scale-resolving simulations typically rely on explicit time-stepping schemes due to low computational cost per time step. In this work, we investigate an implicit time-stepping scheme that increases the computational cost for each time step, but permits larger time steps to reduce the time-to-solution. In particular, we study a velocity correction scheme that is commonly employed for solving the incompressible Navier-Stokes equations. The semi-implicit velocity correction scheme uses implicit diffusion and explicit advection treatment. The explicit advection treatment becomes a performance bottleneck for high Reynolds number flows around complex geometries, because of a CFL-type condition that constrains the algorithm’s stability to small time steps. We explore a linear-implicit velocity correction scheme which removes the CFL limitation. The linear-implicit scheme uses a linearisation of the advection operator and, hence, preserves the linear structure of the semi-implicit algorithm. We perform a comparison of both velocity correction schemes and look into their stability, accuracy and computational performance. Our investigation includes canonical problems and a two-dimensional cylinder flow for verification. Further, we investigate turbulent flows at high Reynolds number and around challenging geometries based on Formula 1 race cars. We find that the linear-implicit scheme allows strong improvements in the stability allowing up to 100-times larger time step sizes on the most complex 3D geometry. The influence on the accuracy with larger time step sizes varies and all cases show negligible differences up to at least 10-times larger time step sizes. Additionally, the stability improvement provides leverage for the computational performance enabling 2-fold speed-up with minor loss in accuracy and 10-fold speed-up in time-to-solution with stronger losses in the accuracy.
2023
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@phdthesis{2023:slaughter:spectralhp, author = {Slaughter, James}, title = {Spectral/hp element methods for industrial applications: flow past inverted wings in ground effect}, school = {Imperial College London}, year = {2023}, url = {http://hdl.handle.net/10044/1/110347}, doi = {10.25560/110347}, groups = {thesis} }Computational Fluid Dynamics (CFD) is the basis of most modern industrial aerodynamic pipelines. With increased reliance on CFD processes, the demands on the accuracy and fidelity of the codes, grow hand-in- hand. When considering complex industrial flows, like those considered in automotive and motorsports applications, the accuracy and fidelity of traditional turbulence models like Reynolds Averaged Navier Stokes and Detached Eddy Simulation and the efficiency of legacy low- order spatial discretisations come into question. High-order techniques, like Spectral/hp Element Methods, offer distinct advantages in computational efficiency, hoping to bridge the gap and make higher-fidelity scale-resolving techniques such as Large Eddy Simulation more accessible to the average engineer. This thesis is presented in two parts. The first part investigates the current state-of-the-art of Spectral/hp Element methods. It uses industrial benchmarks including the SAE Notchback body and the Imperial Front Wing to highlight some of the restrictions of the methodology towards wider industrial applications. Some of the restrictions highlighted include the meshing intricacies in mixed h/p approaches, geometric and meshing issues, purely explicit advection schemes, stabilisation and algorithmic constraints including preconditioning. The second part looks at the benchmark cases. It focuses on inverted wings in ground effect. A single element in ground effect, the GA(W)-1 profile was studied with and without freestream forcing at 0,3,5 degree angles of attack. It was noted that the freestream forcing changed the transition mechanism - highlighting the need for freestream noise in resolved simulations. Finally, a multi-element front wing was studied utilising the Imperial Front Wing geometry at a ride height of 0.36h/c initially. Intergral quantities and spatial distributions, along with studies investigating the spanwise width using auto-correlation and the interplay between transition mechanisms using cross-spectral phase presented. Ride height was then swept and frequency analysis presented showing the implications on key flow structures. -
@phdthesis{2023:lyu:three-dimensional, author = {Lyu, Ganlin}, title = {Three-dimensional discontinuous spectral/hp element methods}, school = {Imperial College London}, year = {2023}, url = {http://hdl.handle.net/10044/1/109239}, doi = {10.25560/109239}, groups = {thesis} }The prediction of laminar boundary layer transition is still under intensive investigations in the fluid instability community, particularly when complicated factors (e.g realistic geometries) are involved. In this thesis we introduce an open-source and unified framework for boundary layer transition analysis at transonic conditions and over wing sections where surface irregularities may present. Different computational tools are integrated in the framework, and therefore overcomes the difficulties of two separate and usually quite disparate processes, i.e. the computation of baseflow and disturbances, when using eN transition prediction method. To reduce the computational cost, a near-body reduced domain is adopted with boundary conditions enforced to be compatible with a computationally cheaper three-dimensional (3D) RANS simulation. It is desirable to enforce a consistent pressure distribution. However, the pressure compatibility is not typically the case when using the standard Riemann inflow boundary condition, while not all modified boundary condition enforcements lead to a stable simulation. We therefore revisit the Riemann problem adopted in many DG-based high-fidelity formulations and develop a useful analysis approach to construct boundary conditions for the inviscid term based on a linearized one-dimensional model. In-depth analysis and results are also presented. We next apply this analysis framework to investigate the transition performance using a wing section of CRM-NLF model for both clean and gapped geometries. In 3D gapped case, we find self-sustained oscillations in the small-sized gap which excites travelling waves. An incompressible swept plate flow is simulated to investigate the hydrodynamic instability that drives the oscillation inside the gap. It is found that the traveling waves correspond to a BiGlobal mode inside the gap and possess a convective nature. This new discovery suggests the presence of different physics compared with a gapped non-swept case, and thus motivates our in-depth investigations in future works. -
@phdthesis{2023:frey-marioni:machine, author = {Frey Marioni, Yuri}, title = {A machine learning approach to develop turbulence closures using clustering and neural networks}, school = {Imperial College London}, year = {2023}, url = {https://hdl.handle.net/10044/1/122801}, doi = {10.25560/122801}, groups = {thesis} }Modelling the effect of turbulence, rather than resolving all turbulent scales, is still the most common approach to Computational Fluid Dynamics (CFD) in the Aerospace industry. This is generally achieved solving the Reynolds Averaged Navier-Stokes (RANS) equations, which introduce additional unknown variables and require turbulence models for closure. Many of such models were developed decades ago and calibrated against several canonical cases, aiming at general purpose models of wide applicability. As a consequence of this there are areas where RANS predictions have been proven to be particularly weak. Accuracy in predictions is essential for several reasons: it ensures that designers are directed towards the optimal regions of novel design spaces; it limits the cascade of errors when running multi-modular and integrated CFD calculations; it provides more confidence in extracting the numbers directly out of the CFD solution, as opposed to only reading trends and qualitative behaviours. In this thesis a different approach is investigated: it consists in combining high-fidelity CFD calculations, accurate and able to generate large amount of data, with Machine Learning (ML) algorithms, the ideal tool to find correlations and relate turbulence behaviour to mean flow features. The output of the process is a data-driven turbulence closure that can easily be implemented in a CFD solver and provide more accurate flow predictions, at the same cost of a traditional RANS calculation. First, a Framework is developed from simple test cases to define the data extraction and training procedures. This includes the use of Clustering to select training areas and Artificial Neural Networks (ANN) to learn the turbulence closure. Subsequently, the Framework is applied to more complex and industry-relevant flows. It is believed that whilst a universal model, able to cover all flows, might not be achievable, a library of closures that improve predictions on specific applications is a very appealing industrial design tool.
2022
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@phdthesis{2022:reavette:improved, author = {Reavette, Ryan}, title = {Improved pulse wave analysis for diagnosing and monitoring heart}, school = {Imperial College London}, year = {2022}, url = {http://hdl.handle.net/10044/1/98152}, doi = {10.25560/98152}, groups = {thesis} }Heart failure is treatable, but in the United Kingdom, the one-, five- and ten-year mortality rates are 24.1, 54.5 and 75.5%, respectively. The poor prognosis reflects, in part, the lack of specific, simple and affordable diagnostic techniques: the disease is often advanced by the time a diagnosis is made. Moreover, 79% of UK heart failure diagnoses are made only after an emergency hospital admission despite 41% of patients visiting their GP in the preceding five years with at least one the main symptoms of heart failure, breathlessness, fatigue or ankle swelling. The survival rates following a diagnosis in primary care are, as expected, better than the average, but there are clear missed opportunities for early diagnosis and intervention. There is also a significant disconnect between clinical guidelines and actual patient diagnoses: between 2010 and 2013, only 24% of UK patients were diagnosed according to the pathway recommended by the European Society of Cardiology. All of these factors necessitate an improved diagnosis pipeline. Arterial waves carry information about the performance of the heart and vessels, and previous studies have demonstrated that certain metrics derived from pressure velocity based wave intensity analysis are significantly altered in the presence of heart failure. The pressure wave-form, however, can only be obtained accurately using invasive methods, which has inhibited clinical adoption. This thesis investigates the potential for a new form of wave intensity, based instead on noninvasive ultrasound measurements of arterial diameter and velocity, to improve the heart failure diagnosis pipeline. Diameter and pressure are intrinsically related, but this relationship is fundamentally nonlinear, as the arterial wall exhibits properties such as viscoelasticity and strain stiffening. Through one-dimensional computational modelling of blood flow in a virtual population of 600 people, this thesis has shown the two forms of wave intensity are similar regardless of these nonlinearities. Using a second virtual population of 2000 people, with half modelled as healthy controls and half with heart failure through an impaired stroke volume, this thesis has also shown that, when analysed with machine learning-based classification techniques, metrics derived from this diameter-based wave intensity can identify heart failure in individual patients with 99% recall and 95% precision. Computational results must be corroborated with experimental findings before they can be truly accepted. This thesis also, therefore, describes a first-in-man trial where ultrafast ultrasound-based measurements of wave intensity were made in controls and heart failure patients. Statistically significant differences were identified in multiple wave intensity metrics representative of both systolic and diastolic function; the results are promising regarding the introduction of noninvasive wave intensity to the clinic. -
@phdthesis{2022:pan:implicit, author = {Pan, Yu}, title = {Implicit time integration for high-order compressible flow solvers}, school = {Imperial College London}, year = {2022}, url = {http://hdl.handle.net/10044/1/101219}, doi = {10.25560/101219}, groups = {thesis} }The application of high-order spectral/hp element discontinuous Galerkin (DG) methods to unsteady compressible flow simulations has gained increasing popularity. However, the time step is seriously restricted when high-order methods are applied to an explicit solver. To eliminate this restriction, an implicit high-order compressible flow solver is developed using DG methods for spatial discretization, diagonally implicit Runge-Kutta methods for temporal discretization, and the Jacobian-free Newton-Krylov method as its nonlinear solver. To accelerate convergence, a block relaxed Jacobi preconditioner is partially matrix-free implementation with a hybrid calculation of analytical and numerical Jacobian.The problem of too many user-defined parameters within the implicit solver is then studied. A systematic framework of adaptive strategies is designed to relax the difficulty of parameter choices. The adaptive time-stepping strategy is based on the observation that in a fixed mesh simulation, when the total error is dominated by the spatial error, further decreasing of temporal error through decreasing the time step cannot help increase accuracy but only slow down the solver. Based on a similar error analysis, an adaptive Newton tolerance is proposed based on the idea that the iterative error should be smaller than the temporal error to guarantee temporal accuracy. An adaptive strategy to update the preconditioner based on the Krylov solvers convergence state is also discussed. Finally, an adaptive implicit solver is developed that eliminates the need for repeated tests of tunning parameters, whose accuracy and efficiency are verified in various steady/unsteady simulations. An improved shock-capturing strategy is also proposed when the implicit solver is applied to high-speed simulations. Through comparisons among the forms of three popular artificial viscosities, we identify the importance of the density term and add density-related terms on the original bulk-stress based artificial viscosity. To stabilize the simulations involving strong shear layers, we design an extra shearstress based artificial viscosity. The new shock-capturing strategy helps dissipate oscillations at shocks but has negligible dissipation in smooth regions. -
@phdthesis{2022:hambli:application, author = {Hambli, Walid}, title = {Application of spectral/hp element methods to high-order simulation of industrial automotive geometries}, school = {Imperial College London}, year = {2022}, url = {http://hdl.handle.net/10044/1/103325}, doi = {10.25560/103325}, groups = {thesis} }Flow predictions around cars is a challenge due to massively separated flow and complex flow structures generated. These flow features are usually poorly predicted by present industrial computational fluid dynamics (CFD) codes based on a low fidelity Reynolds averaged Navier Stokes (RANS) approach simulating the mean effects of turbulence. On the other hand, high fidelity approaches resolve turbulent scales but require many more degrees of freedom than classical techniques for an accurate solution. Previous applications have shown that the coupling of the spectral/hp element method and implicit large eddy simulation (iLES) turbulence treatment could be a potential candidate to perform high-fidelity simulations. This work aims at transferring the spectral/hp element technology to the automotive industry in which high Reynolds numbers and complex geometries are typical. Recent developments in stabilisation techniques such as the discontinuous Galerkin kernel spectral vanishing viscosity (SVV) and high-order meshing capabilities open the possibility of the application of the spectral/hp element method to complex cases. The technology is first implemented to an industrial case proposed by McLaren Automotive Limited (MLA) at a realistic Reynolds number of 2,3 million based on the front wheel diameter and is compared to a RANS numerical development tool. Differences in terms of vortical structures arrangement, principally due to the front wheel wake are highlighted. In parallel, a workflow is developed to systematically address similar complex cases. The interaction between h-refinement, related to the size of the elements of the mesh, and p-refinement, corresponding to the polynomial expansion order, is investigated on the SAE notchback body. Two different hp-refinement strategies with similar numbers of degrees of freedom are employed, the first one with a fine mesh and a third-order accurate polynomial expansion and the second one with a coarse mesh and a fifth-order accurate polynomial expansion. Results show that a minimum level of h-refinement is necessary to capture flow features and that p-refinement can subsequently be used to improve their resolution. The final part focuses on wheel rotation modelling. Scale-resolving techniques are intrinsically unsteady and therefore require sophisticated techniques to correctly model rotating wheels. A procedure, built upon an immersed boundary method (IBM) called the smoothed profile method (SPM), is developed to model complex three-dimensional rotating geometries, in particular rim spokes. It is finally applied to an isolated rotating wheel case and results are compared to the moving wall (MW) and the moving reference frame (MRF) modelling techniques. It is concluded that the SPM is in better qualitative agreement with experimental results present in the literature than the two other modelling strategies.
2021
- Z. YanBiBTeX AbstractEfficient implicit spectral/hp element DG techniques for compressible flowsPhD thesis, Imperial College London, 2021. doi 10.25560/98366
@phdthesis{2021:yan:efficient, author = {Yan, Zhenguo}, title = {Efficient implicit spectral/$hp$ element DG techniques for compressible flows}, school = {Imperial College London}, year = {2021}, groups = {thesis}, doi = {10.25560/98366} }In the simulation of stiff problems, such as fluid flows at high Reynolds numbers, the efficiency of explicit time integration is significantly limited by the need to use very small time steps. To alleviate this limitation and to accelerate compressible flow simulations based on high-order spectral/hp element methods, an implicit time integration method is developed using singly diagonally implicit Runge-Kutta temporal discretization schemes combined with a Jacobian-free Newton Krylov (JFNK) method. This thesis studies several topics influencing the efficiency, accuracy and robustness of the solver. Firstly, an efficient partially matrix-free block relaxed Jacobi (BRJ) preconditioner is proposed, in which the Jacobian matrix and preconditioning matrices are properly approximated based on studies of their influences on convergence. The preconditioner only forms and stores the diagonal part of the Jacobian matrix while the off-diagonal operators are calculated on the fly. Used together with techniques such as using single precision data, the BRJ can largely reduce the memory consumption when compared with matrix-based ones like incomplete LU factorization preconditioners (ILU). To further accelerate the solver, influences of different parts of the flux Jacobian on the preconditioning effects are studied and terms with minor influences are neglected. This reduces the computational cost of the BRJ preconditioner by about 3 times while maintaining similar preconditioning effects. Secondly, adaptive strategies for a suitable choice of some free parameters are designed to maintain temporal accuracy and relatively high efficiency. The several free parameters in the implicit solver have significant influences on the accuracy, efficiency and stability. Therefore, designing proper strategies in choosing them is essential for developing a robust general purpose solver. Based on the idea of constructing proper relations between the temporal, spatial and iterative errors, adaptive strategies are designed for determining the time step and Newton tolerance. These parameters maintain temporal accuracy of the solver in the sense that further decreasing temporal and iterative errors will not obviously improve the efficiency. Meanwhile, they maintain relatively efficient by avoiding excessively small time step and Newton tolerance. The strategies are tested in different types of cases to illustrate their performance and generality. Finally, the implicit solver is studied in high-fidelity simulations of turbulent flows based on a hierarchical implementation in the open-source spectral/hp element framework Nektar++. The solver is applied to large-eddy simulations of Taylor-Green vortex flow, turbulent channel flow and flow over a circular cylinder cases. The efficiency of the solver and the prediction accuracy of these problems are studied. The results show that the solver yields good predictions in turbulence simulations whilst keeping good stability and high efficiency. - V. SainiBiBTeX AbstractPerformance and accuracy of high-order accurate large-eddy simulations for gas turbine combustor aerodynamicsPhD thesis, Loughborough University, 2021. doi 10.26174/thesis.lboro.19160864.v1
@phdthesis{2021:saini:performance, author = {Saini, Vishal}, title = {Performance and accuracy of high-order accurate large-eddy simulations for gas turbine combustor aerodynamics}, school = {Loughborough University}, year = {2021}, groups = {thesis}, doi = {10.26174/thesis.lboro.19160864.v1} }The doctoral work compares two numerical approaches, the second-order finite-volume method and a newer high-order (HO) element-based method, for performing scale resolving simulations of industrially-relevant gas turbine combustor (GTC) flow fields. The overarching objective is to provide recommendations to the industrial partner on next-generation combustor simulation methods. Computational fluid dynamics (CFD) plays an important role in physical understanding, design and development of industrial flow devices such as GTCs. The GTCs feature highly unsteady flow features and therefore require computationally-demanding scale resolving simulations for accurate results. In practice, these simulations are predominantly performed using the existing finite-volume (FV) solvers, which are at most second-order accurate and therefore can be considerably inaccurate or expensive. As an alternative, the HO accurate methods are gaining popularity in engineering flow simulations due to their promise of higher accuracy for a given computational cost, or lower cost for a required accuracy. The HO solvers are particularly advantageous for scale resolving simulations of unsteady, vortex dominated flows. This becomes relevant for GTCs where the combustion performance is dominated by the unsteady flow features (similar features are encountered in many other engineering scenarios such as bluff body wakes, high-lift wing configurations and rotor blades). The challenge, however, is that the HO methods are relatively complicated to implement and use for complex industrial geometries on affordable under-resolved grids. Recently, implementations of element-based HO methods, such as spectral-hp and flux-reconstruction, have been developed that are capable of handling complex geometry via hybrid meshes. However, their application to realistic flow cases using under-resolved meshes is still rare. Furthermore, very few studies could be found that evaluate the accuracy vs cost of these methods for practical scale resolving large-eddy simulation (LES). To address this gap, the present work objectively evaluates and analyses the accuracy vs cost of the element-based HO solvers against standard second-order FV solvers for LES of GTC relevant geometries. This quantification may facilitate the use of better methods in industry and academia for not only GTCs but a broader range of vortex-dominated flow applications. The second-order FV and HO LES solvers are compared for fixed cost/accuracy under industrially relevant conditions (complex geometry and under-resolution). The representative open-source packages are employed – the second-order FV solver derives from the OpenFoam framework and the HO solver from the spectral-hp Nektar++ framework. The key differences are in the numerical accuracy and the subgrid scale treatment. The evaluation of accuracy vs cost is undertaken on four cases, two fundamental (inviscid vortex advection, Taylor-Green vortex) and two combustor-related advanced cases. The vortex advection test suggests that polynomial order 4 (P4) provides a good balance of accuracy, cost and numerical stability within the HO solver. Further, under-resolved P4 LES on the Taylor-Green vortex case shows that HO solver is at least 7 times computationally cheaper for a given accuracy level, and 2.5 to 10 times more accurate for a given cost as compared to the second-order solver. In addition, switching to coarser and unstructured meshes is found to lower the HO benefits. The combustor cases focus on two relevant flow features: port flow and swirling flow with mixing. Here, the flow parameters such as Reynolds numbers, flow split and Swirl number are representative of realistic combustors. For both cases, the unsteady data shows that the HO P4 simulations resolve a much broader range of turbulent scales and reproduce the instantaneous flow state better than the second-order simulations for a given cost. This feeds into the mean and rms velocity statistics and the P4 run matches the reference experimental data better in the majority of flow domain. However, the accuracy improvement in mean results of the advanced cases is not always as distinctive as the Taylor-Green vortex case. It is estimated that for a given accuracy, a second-order FV run may cost 3-8 times more as compared to a P4 run. In the swirling flow case, it is additionally found that the HO benefit is higher with hybrid meshes compared to the hexahedral meshes (relevant to industry). For each case, the differences observed in the flow-fields are explained using a kinetic energy dissipation rate analysis. It is found that the improvement from HO solver is mainly due to lower numerical dissipation and the subgrid scale treatment plays a secondary role. As a first step towards combustion simulations, a passive scalar transport equation is solved in the swirler case (the scalar mimics a conserved quantity such as the mixture fraction). The solvers are extended to incorporate this additional equation. The improvement from the HO solver in scalar field results is less significant as compared to that of the velocity field. This shortfall is partly attributed to the high Schmidt number ( 3000) from the reference experiment, for which the current scalar stabilisation technique in the high-order solver needs further improvement. Nevertheless, it is likely that for gaseous mixing (where Schmidt number is around unity) there would be considerable benefit from HO in mixing and reacting flow LES due to better resolution of small turbulent scales. The work shows that adopting HO methods for practical turbulent combustion system applications is highly likely to provide considerable accuracy/cost benefits. It also highlighted that improvements in high-order mesh generation and scalar boundedness would be required to mature the HO solvers for realistic combustion configurations. -
@phdthesis{2021:eichstadt:portable, author = {Eichstadt, Jan Robert}, title = {Portable shared-memory parallelisation strategies for high-order finite element codes}, school = {Imperial College London}, year = {2021}, groups = {thesis}, url = {http://hdl.handle.net/10044/1/86621}, doi = {10.25560/86621} }This thesis investigates strategies to parallelise numerical simulation software frameworks in the context of high-order finite element solvers. Due to the recent evolution of high performance computing (HPC) hardware from single-core central processing units (CPUs) to multi-core CPUs and the emergence of general purpose graphics processing units (GPGPUs or short GPUs), these shared memory systems are now characterised by a high degree of parallelism. They also possess a variety of architecture-specific features that must be appropriately utilised in order to fully realise their capabilities. Large-scale legacy solver frameworks thus face the question how to adapt their codebase in the most effective way, to enable performance and portability across a heterogeneous landscape of parallel HPC systems, while ensuring code maintainability. Various approaches to address this challenge are considered using practical investigations of core numerical algorithms for high-order finite element methods in order to ensure representative performance profiles. The selected core algorithms are a parallel mesh-optimisation method that optimises elemental shapes by minimising a deformation energy, and an implicit solver of the Helmholtz equation which forms the computationally most demanding part of a complete incompressible Navier-Stokes solver. Overall the results presented here clearly demonstrate that algorithmic adaptations have to be introduced to enable execution on modern CPU and GPU systems and to achieve reasonable performance. Key aspects for an efficient mapping of the algorithms onto the hardware are considered: colouring approaches in connection with reduction operations, alongside determining the most effective manner of utilising multi-level nested parallel algorithms on multi-level parallel shared-memory hardware. It is further shown that the layout of data structures and their placement in memory is often the most important aspect in improving performance for both CPU and GPU systems. In order to achieve efficient memory access over vectorised operations, an interleaved data layout is developed. In a novel approach for elemental evaluations that minimises memory bandwidth, performance profiling demonstrates that on GPUs faster runtimes can be achieved, despite additional arithmetic operations. The balance between the utilisation of different hardware systems is assessed using runtimes, performance modelling, and a novel operational cost metric, and demonstrates that executions of the investigated algorithms on GPUs are both faster and more cost-effective than on CPUs for the problems under consideration. Apart from the algorithmic adaptations, two programming paradigms are investigated: the effectiveness and performance of a single codebase, augmented with a variety of of portable programming models is compared against the implementation of a small number of hardware-specific kernels in regions of computational hotspots. The analysis here suggests that although the considered portable programming models (OpenMP, OpenACC, and Kokkos) should be easier to maintain, robust compiler support for all hardware types and unambiguous interpretation of compiler directives is not always guaranteed. The investigated GPU-specific CUDA kernels are most performant and achieve two to three times faster runtimes than all other models. Further work is proposed to follow the second paradigm in order to efficiently parallelise large software frameworks for high-order flow solvers. -
@phdthesis{2021:duran:stability, author = {Duran, Matt}, title = {The Stability of Two-Dimensional Cylinder Wakes in the Presence of a Wavy Ground}, school = {University of Central Florida}, year = {2021}, groups = {thesis}, url = {https://stars.library.ucf.edu/cgi/viewcontent.cgi?article=2088&context=honorstheses} }The following study investigates hydrodynamic stability for two-dimensional, incompressible flow past a cylinder and compares it alongside four different variations of a wave-like ground introduced within the wake region of the cylinder wake. These different variations include changing the distance of the cylinder both horizontally from the wave-like structure and vertically from the ground. The geometry and meshes were initially constructed using GMSH and imported into Nektar++. The baseflows were then obtained in Nektar++ using the Velocity Correction Scheme, continuous Galerkin method, and Unsteady Navier Stokes solver. Then, the Implicitly Restarted Arnoldi Method driver was used to retrieve the various eigenvalues/eigenmodes and growth rates. Finally, the results were visualized in Paraview which allowed clear comparisons between the stability of the flow between each case. The findings obtained show a clear effect on stability when considering different cases, for a plain cylinder and for each case there are observations to be made in how the various eigenmodes varied in terms of magnitude and shape, other observations were made in the differing critical Reynolds number and frequencies among the cases. This study is relevant to various natural environments where a blunt object may come in range of a bumpy or wavy ground. In these scenarios it can be important to monitor how instabilities propagate and cause effects such as turbulence or drag. Additionally, investigation like these can detail how to effectively avoid undesirable characteristics of instability. -
@phdthesis{2021:cassinelli:spectralhp, author = {Cassinelli, Andrea}, title = {A spectral/$hp$ element {DNS} study of flow past low-pressure turbine cascades and the effects of inflow conditions}, school = {Imperial College London}, year = {2021}, groups = {thesis}, url = {http://hdl.handle.net/10044/1/103146}, doi = {10.25560/103146} }The combined rapid progress of hardware capability and the development of cutting-edge numerical methods have recently provided an opportunity for Computational Fluid Dynamics to be inserted in the design loop, with the role of a virtual wind tunnel. This thesis tackles the development of a validated incompressible Direct Numerical Simulation capability to model complex configurations of interest for the turbomachinery Industry, adopting for the first time the spectral/hp element methods implemented in the Nektar++ software framework. First, an extensive analysis of the numerical convergence properties is carried out on an open geometry with clean inflow boundary conditions, to establish a set of best practices and relate accuracy and computational cost. Subsequently, the effect of stochastic and deterministic unsteadiness is analysed in detail, with particular focus on various methodologies to provide physical disturbances, their computational cost and accuracy with respect to reference experimental data. The findings are extended to a range of Reynolds numbers representative of realistic operating conditions, with focus on traditional performance indicators but also unsteady statistics to provide rich insight into the suction surface transition mechanism, which plays a crucial role in the generation of profile losses. As a result, a detailed characterisation of the flow physics is provided in a range of inflow conditions and Reynolds numbers. Excellent agreement with high fidelity experimental data is achieved especially at moderate and high Reynolds numbers, supporting the use of these methodologies in Industry as a preliminary standalone investigation tool. -
@phdthesis{2021:basso:analytical, author = {Basso, Robin Lucas Guillaume}, title = {The analytical and phenomenological sensitivity study of the flow-induced instabilities about a hinged circular cylinder with a splitter}, school = {Imperial College London}, year = {2021}, groups = {thesis}, url = {http://hdl.handle.net/10044/1/108170}, doi = {10.25560/108170} }This thesis investigates the origin of flow-induced instabilities and their sensitivities in a flow over a rotationally flexible circular cylinder with a rigid splitter plate. A linear stability and sensitivity problem are formulated in the two-dimensional Eulerian frame by considering the geometric nonlinearity arising from the translations and rotational motion of an arbitrary geometry (cross-sectional structure’s shape), which is not present in the stationary or purely translating stability methodology. This nonlinearity needs careful and consistent treatment in the linearised problem, particularly when considering the Eulerian frame of reference adopted in this study and not so widely considered. Considering the one degree of freedom problem of the rotationally flexible circular cylinder with a rigid splitter plate, two types of instabilities arising from the fluid-structure interaction are found. The first type of instability is the stationary symmetry-breaking mode, which was well reported in previous studies. This instability exhibits a strong correlation with the length of the recirculation zone. A detailed analysis of the instability mode and its sensitivity reveals the importance of the flow near the tip region of the plate for the generation and control of this instability mode. The second type is an oscillatory torsional flapping mode, which has not been well reported. This instability typically emerges when the length of the splitter plate is sufficiently long. Unlike the symmetry breaking mode, it is not so closely correlated with the length of the recirculation zone. However, the sensitivity analysis also reveals the crucial role played by the flow near the tip region in this instability. Finally, it is found that many physical features of this instability are reminiscent of those of the flapping (or flutter instability) observed in a flow over a flexible plate or a flag, suggesting that these instabilities share the same physical origin. The sensitivity analysis of both the symmetry breaking and flapping instability is also compared to the results obtained from a stationary circular cylinder fitted to a splitter plate of the same lengths. Physically meaningful analogies are noted between the sensitivity regions of the three instabilities.
2020
- E. CookeBiBTeX AbstractModelling the effect of step and roughness features on swept wing boundary layer instabilitiesPhD thesis, Imperial College London, 2020. doi 10.25560/83744
@phdthesis{2020:cooke:modelling, author = {Cooke, Emma}, title = {Modelling the effect of step and roughness features on swept wing boundary layer instabilities}, school = {Imperial College London}, year = {2020}, groups = {thesis}, doi = {10.25560/83744} }Destabilisation effects of forward facing steps, backward facing steps and bumps on stationary and travelling crossflow disturbances are investigated computationally for a 40 degree infinitely swept wing. Step and bump heights range from 18% to 82% of the boundary layer thickness and are located at 3%, 10% and 20% chord. The spectral/hp element solver, Nektar++, is used to compute base flow profiles with an embedded swept wing geometry. Parabolised Stability Equations (PSE) and Linearised Harmonic Navier-Stokes (LHNS) models are used to evaluate growth of convecting instabilities. The presence of surface step features impose an extremely rapidly varying flow field locally, which requires accurate resolution of the perturbed flow field. Derivations of these PSE and LHNS models incorporating the excrescence (PSEh, LHNSh) are elucidated. Unlike the PSE, which suffer from a stream-wise numerical step size restriction, the LHNS are a fully elliptic set of equations which may use an arbitrarily fine grid resolution. Unsurprisingly, the PSE codes fail to capture the effect of abrupt changes in surface geometry introduced by the step features. Results for the LHNS and roughness incorporating LHNSh are given for the varying vertical step and ramped type steps. Comparisons are made between the LHNSh model and direct numerical simulations involving the time-stepping linearised Navier-Stokes solver (NekLNS) in the Nektar++ software framework. Most previous work in the topic area has focused on Tollmien-Schlichting perturbations over two-dimensional flat plate flows or aerofoils, the novelty of this work lies with analysing crossflow instability over a swept wing boundary-layer flow with step features. PSEh and LHNSh models are tested with convecting Tollmien Schlichting instability over a dimple and randomly distributed roughness on an overall flat plate flow. The dimple case performs very well whereas it is more difficult to obtain converged results with the random roughness case, likely due to large stream-wise velocity gradient changes. A 45degree ramped shape roughness is investigated and remarkably good agreement between the LHNSh solution and NekLNS solution is found. Forward facing ramps and steps are found to act as greater amplifiers with increased height, whilst backward facing ramps and steps predict very weak changes in the disturbance development. This is contrary to the wider literature and an argument is made that backward facing steps and ramps initiate an immediate non-linear interaction which cannot be captured with linear theory. Vertical forward facing step cases also predict greater amplification with increased step height, which is not observed in the backward facing step cases. Again, this is believed to be due to non-linear mode interaction that is immediately triggered by the step. Bump roughness cases agree well qualitatively with experimental work on a 40 degree swept wing, the AERAST geometry. Good agreement locally to the roughness could not be drawn with the NekLNS solutions, likely due to the presence of strong stream-wise gradients and mesh limitations.
2019
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@phdthesis{2019:yadav:hydrodynamic, author = {Yadav, Nikesh}, title = {Hydrodynamic instability and mixing enhancement in grooved channels}, school = {The Institute of Aeronautics and Applied Mechanics}, year = {2019}, groups = {thesis}, url = {https://repo.pw.edu.pl/info/phd/WUT85cac1229c164a368658c938338491d2/} }Operation of different flow-based devices, such as blood oxygenators, compact heat exchangers or dialyzers can be greatly improved by decreasing hydraulic losses and increasing achievable mixing efficiency. A relatively uninvestigated approach to both mixing enhancement and decreasing hydraulic losses can be achieved by large scale grooving of flow boundaries. Recently, it has been shown that grooves aligned longitudinally with respect to flow could lead to strong destabilization and, at the same time, provide drag decreasing potential. The thesis explores the possibility of utilizing such grooves as a promising method of mixing enhancement and drag reduction. Thesis describes flow dynamics emerging due to the transverse modulation of the walls (longitudinal grooves). The content of this thesis focuses on low Reynolds numbers, where flows are generally laminar. The primal goal is to establish channel geometries that enhance achievable mixing at possibly low drag increase. Numerical investigations are performed with the DNS approach using the spectral element method implemented in the package Nektar++. The analysis begins with the investigation of the flow dynamics in the channel with periodic sinusoidal walls and infinite width. Then, the flow in the finite-width rectangular duct with corrugated top and bottom wall has been studied. Later, flow dynamics of various groove shapes such as triangular, square and trapezoidal ones, are compared and the influence of the Fourier contents of the geometrical shape of the groove on the drag reduction and destabilization potential has been examined. The thesis is concluded with both the qualitative and quantitative characterization of mixing due to nonlinear saturation of identified instabilities. - F. Fabian BuscarioloBiBTeX AbstractSpectral/hp large eddy simulation of vortex-dominated automotive flows around bluff bodies with diffuser and complex front wing geometriesPhD thesis, Imperial College London, 2019. doi 10.25560/110789
@phdthesis{2019:fabian-buscariolo:spectralhp, author = {Fabian Buscariolo, Filipe}, title = {Spectral/hp large eddy simulation of vortex-dominated automotive flows around bluff bodies with diffuser and complex front wing geometries}, school = {Imperial College London}, year = {2019}, groups = {thesis}, doi = {10.25560/110789} }In this research project, it is demonstrated the use of spectral/hp element method for simulations of fully 3D complex geometries. Such solutions at high Reynolds numbers and with higher order polynomials were previously intractable due to numerical stability issues affecting the convergence of the scheme. For this approach, we have employed the latest development of continuous Galerkin spectral vanishing viscosity (CG-SVV) with a discontinuous Galerkin (DG) mimicking kernel. Together with dealiasing techniques, the numerical stability and convergence characteristics of the spectral/hp element method have been greatly improved. These advances in numerical methods are also supported by novel meshing strategies, taking advantage of the additional flexibility in changing the uniform polynomial orders of the mesh and the solution. As a result, efficient simulations can be formulated with consistent and highly accurate solutions obtainable. Specific for this work, the focus is on complex geometries often found in automotive engineering. To reduce the computational demands, this research explored the use of symmetry boundary conditions for large eddy simulations (LES) using a half model. It is found that if only the average flow properties near the body are of interest, such an approach can provide more than 50% reduction in simulation time while maintaining the solution quality. In terms of improving the solution resolution, as one might expect from a p-type method we have observed that increasing the polynomial order can be a more effective approach in comparison to conventional mesh refinement. In the three test cases, we have successfully exploited the use of polynomial accuracy of 4th, 5th and 6th order. This is the first comprehensive study using polynomials of such high orders, and the corresponding solutions are obtained for fully 3D geometries using spectral/hp element method. Three test cases have been considered, the first being the simulations of the original Ahmed Body serves as a validation study for 3D simulations of the spectral/hp element method. The Ahmed Body is one of the most widely studied bluff bodies used for automotive conceptual studies and computational fluid dynamics (CFD) software validation. For this validation study, the differences in results obtained using various polynomial orders for the mesh as well as for the solution interpolation have been examined in detail. With the proposed approach, we were able to obtain fairly good correlations with the aerodynamic quantities for polynomial orders of 5 and above. Regarding the flow features around the body, solutions from the 6th order polynomial showed clear advantage in the slant vortex intensity. With the computational facilities, further increase of solution polynomial order is not feasible; however, the required solution resolution can also be obtained via the use of local mesh refinement. We determine that this level of solution accuracy, after comparing with various studies in the literature, cannot be obtainable using steady-state simulations such as the very popular Reynolds averaged Navier-Stokes (RANS) method. Based on the validation result, the second test case involved the simulations of Ahmed Body geometries with a simplified diffuser using the proposed method. This case serves as an independent study examining the suitability of the method for design analysis. Using the same 6th order polynomial and Refined mesh, the solution successfully identified the flow features consistent with to past literature on underbody diffusers. Additionally, we have found that the geometry of the reference body imposes a quite significant influence on the performance of the diffuser, as well as identified some strong interplay between the lower-side vortex and the diffuser flow. The toolchain has clearly demonstrated its capability in assisting integrated design analysis for a simplified road vehicle equipped with a diffuser. In the final test case, a new benchmark study case for aerodynamic design of high-performance vehicles and racing cars, the Imperial front wing is proposed. This study consists of a multi-element front-wing based on a Formula One front wing design. It generates complex flow features including ground effects, and multiple vortex system development and interaction. We used this test case as a challenging examination of our proposed method and simulation strategy using the spectral/hp element method. The simulations were also supported by an independent experimental study and results obtained for comparison achieved a high level of agreement. Using a polynomial order of 4th and above have successfully correlated the flow velocity fields at various planes downstream, while increasing the polynomial order to 5th will further result in a good matching of flow visualisation details. From all three test cases, the spectral/hp element method when applied to suitable meshes at reasonably polynomial orders has been able to accurately and consistently yield reliable solutions in good agreement with experiment. The benefits of using high order polynomials for mesh generation of complex geometries, and for solution interpolation of higher accuracy have enabled the use of much coarser meshes than would typically be applied in commercial CFD codes. The progress made in this research is a solid step forward for the adaptation of the spectral/hp element for industrial level applications.
2017
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@phdthesis{2017:moura:on, author = {Moura, Rodrigo Costa}, title = {On the use of spectral element methods for under-resolved simulations of transitional and turbulent flows}, school = {Imperial College London}, year = {2017}, groups = {thesis}, url = {http://hdl.handle.net/10044/1/55917}, doi = {10.25560/55917} }The present thesis comprises a sequence of studies that investigate the suitability of spectral element methods for model-free under-resolved computations of transitional and turbulent flows. More specifically, the continuous and the discontinuous Galerkin (i.e. CG and DG) methods have their performance assessed for under-resolved direct numerical simulations (uDNS) / implicit large eddy simulations (iLES). In these approaches, the governing equations of fluid motion are solved in unfiltered form, as in a typical direct numerical simulation, but the degrees of freedom employed are insufficient to capture all the turbulent scales. Numerical dissipation introduced by appropriate stabilisation techniques complements molecular viscosity in providing small-scale regularisation at very large Reynolds numbers. Added spectral vanishing viscosity (SVV) is considered for CG, while upwind dissipation is relied upon for DG-based computations. In both cases, the use of polynomial dealiasing strategies is assumed. Focus is given to the so-called eigensolution analysis framework, where numerical dispersion and diffusion errors are appraised in wavenumber/frequency space for simplified model problems, such as the one-dimensional linear advection equation. In the assessment of CG and DG, both temporal and spatial eigenanalyses are considered. While the former assumes periodic boundary conditions and is better suited for temporally evolving problems, the latter considers inflow / outflow type boundaries and should be favoured for spatially developing flows. Despite the simplicity of linear eigensolution analyses, surprisingly useful insights can be obtained from them and verified in actual turbulence problems. In fact, one of the most important contributions of this thesis is to highlight how linear eigenanalysis can be helpful in explaining why and how to use spectral element methods (particularly CG and DG) in uDNS/iLES approaches. Various aspects of solution quality and numerical stability are discussed by connecting observations from eigensolution analyses and under-resolved turbulence computations. First, temporal eigenanalysis of DG method is revisited and a simple criterion named "the 1% rule" is devised to estimate DG effective resolution power in spectral space. This criterion is shown to pinpoint the wavenumber beyond which a numerically induced dissipation range appears in the energy spectra of Burgers turbulence simulations in one dimension. Next, the temporal eigenanalysis of CG is discussed with and without SVV. A modified SVV operator based on DG’s upwind dissipation is proposed to enhance CG’s accuracy and robustness for uDNS / iLES. In the sequence, an extensive set of DG computations of the inviscid Taylor-Green vortex model problem is considered. These are used for the validation of the 1% rule in actual three-dimensional transitional / turbulent flows. The performance of various Riemann solvers is also discussed in this infinite Reynolds number scenario, with high quality solutions being achieved. Subsequently, the capabilities of CG for uDNS/iLES are tested through a complex turbulent boundary layer (periodic) test problem. While LES results of this test case are known to require sophisticated modelling and relatively fine grids, high-order CG approaches are shown to deliver surprisingly good quality with significantly less degrees of freedom, even without SVV. Finally, spatial eigenanalyses are conducted for DG and CG. Differences caused by upwinding levels and Riemann solvers are explored in the DG case, while robust SVV design is considered for CG, again by reference to DG’s upwind dissipation. These aspects are then tested in a two-dimensional test problem that mimics spatially developing grid turbulence. In summary, a point is made that uDNS/iLES approaches based on high-order spectral element methods, when properly stabilised, are very powerful tools for the computation of practically all types of transitional and turbulent flows. This capability is argued to stem essentially from their superior resolution power per degree of freedom and the absence of (often restrictive) modelling assumptions. Conscientious usage is however necessary as solution quality and numerical robustness may depend strongly on discretisation variables such as polynomial order, appropriate mesh spacing, Riemann solver, SVV parameters, dealiasing strategy and alternative stabilisation techniques. - J.-E. LombardBiBTeX AbstractA high-fidelity spectral/hp element LES study of Formula 1 front-wing and exposed wheel aerodynamicsPhD thesis, Imperial College London, 2017. doi 10.25560/68250
@phdthesis{2017:lombard:high-fidelity, author = {Lombard, Jean-Eloi}, title = {A high-fidelity spectral/hp element LES study of Formula 1 front-wing and exposed wheel aerodynamics}, school = {Imperial College London}, year = {2017}, groups = {thesis}, url = {http://hdl.handle.net/10044/1/68250}, doi = {10.25560/68250} }Computational fluid dynamics is the test bed, for in-silico experiments, before a part is first built however the state-of-the-art relies on low-order Reynolds averaged Navier-Stokes (RANS) or Detached Eddy Simulations (DES) and their turbulence models that require fine tuning of many parameters. They are ill-suited for tackling the complex interaction between the wake of a Formula One front wing and the highly unsteady bluff-body wake of the rolling wheel. This thesis describes the effort made towards assessing the spectral/hp element LES as an alternative method for better for informing the process of the aerodynamicists. Results from the computation of the flow on a rounded wingtip give further insight into the complexity of the flow revealing numerous vortical structures merging into a trailing vortex. A direct numerical simulation of the unsteady wake of an idealised rolling wheel reveals the flow structures associated to the shedding at the top of the wheel, the symmetry breaking as well as the meandering of the jetting-vortices adding to our fundamental understanding of the wheel wake. In particular the DNS allows for a thorough survey of the wake structures in the immediate wake, less than half a diameter, both the jetting vortices and the shedding at the top of the wheel occur but experiments struggle to instrument. Finally preliminary results for the computation of the flow about the front-section of the MP4-17D are reported and compared to experimental results as well as state-of-the-art RANS computation. The CAD geometries, the mesh and initial conditions as well as the exact code used to run them are made openly available for each of the cases reported in this thesis for the fluids community to continue building on these results.
2016
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@phdthesis{2016:serson:numerical, author = {Serson, Douglas}, title = {Numerical study of wings with wavy leading and trailing edges}, school = {Imperial College London}, year = {2016}, url = {http://hdl.handle.net/10044/1/56681}, doi = {10.25560/56681}, groups = {thesis} }Inspired by the pectoral flippers of the humpback whale, the use of spanwise waviness in wings has been considered in the literature as a possible way of delaying the stall, and possibly also reducing the drag coefficient, allowing for improved aerodynamic characteristics. In order to provide a better understanding of this flow control mechanism, the present work investigates numerically the effect of the waviness on the flow around infinite wings with a NACA0012 profile. The study consists of direct numerical simulations employing the spectral/hp method, which is available through the nektar++ library. Considering the high computational cost of the simulations performed, several improvements were introduced to the method, making it more efficient and allowing higher Reynolds numbers to be analysed. These improvements to the method include a coordinate transformation technique to treat the waviness, changes to the parallelism strategy, and an adaptive polynomial order refinement procedure. Initially, simulations were performed for a very low value of the Reynolds number Re=1,000, allowing the three-dimensional flow structures to be observed in detail. In this case, the results show that the waviness leads to a decrease in the lift-to-drag ratio, accompanied by a strong reduction in the fluctuations of the lift force. The reduction in the lift-to-drag ratio is the combined effect of lower drag and lift forces, and is associated with a regime where the flow remains attached behind the peaks of the leading edge while there are distinct regions of flow separation behind the troughs. Then, simulations with Re=10,000 were considered. For high angles of attack, the results for this case are similar to the lower Re, with the waviness leading to separation behind the troughs and reducing both the lift and the drag. However, for a lower angle of attack the waviness leads to a large increase in the lift coefficient. This was observed to be related to the fact that flow around the straight wing is laminar in this case, with the waviness inducing transition to a turbulent state. Finally, the case Re=50,000 was considered, with the results showing a good agreement with experiments presented in the literature. -
@phdthesis{2016:mohamied:multidirectional, author = {Mohamied, Yumnah}, title = {Multidirectional near-wall flow in arteries and its spatial correlation with atherosclerosis}, school = {Imperial College London}, year = {2016}, url = {http://hdl.handle.net/10044/1/44374}, doi = {10.25560/44374}, groups = {thesis} }Atherosclerotic lesions develop non-uniformly throughout the arterial system and their distribution around branches changes with age. This thesis investigates whether multidirectional blood flow, characterised by the transverse wall shear stress metric (transWSS), is related to the initiation of atherosclerosis. The spectral/hp element method was used to simulate pulsatile blood flow in immature and mature rabbit aortic geometries obtained by microCT of vascular corrosion casts. Bootstrapping was used to quantitatively correlate spatial maps around intercostal branch ostia, and found that the low/oscillatory shear theory did not correlate with disease, and could not account for age-related changes in macromolecule uptake. However, evidence for the multidirectional theory was found: transWSS related strongly and positively with disease at both ages and with wall permeability in young rabbits. The pulsatility of the blood is necessary for the existence of multidirectionality, yet the precise nature of the cardiac waveform did not dominantly influence both the large- and small-scale pattern of transWSS. Simulations in partially-idealised vessels revealed that geometry instead was crucial. Vessel curvature was responsible for a Dean vortex pair, whose changing strength over the cardiac cycle created changes in the shear direction at the wall, resulting in two large-scale axial streaks of high transWSS. Vessel torsion determined the asymmetry in their strengths and spatial locations over the descending aorta. Two distributions of transWSS resembling the age-dependent lesion patterns were identified at the individual-branch level, but which arose equally in both age groups. The small-scale patterns were found to depend on the branch’s location with respect to the large-scale streaks, and therefore primarily on torsion, for which no statistically significant difference between age groups was found. Multidirectional flow relates well to disease at the aggregate-level and may explain age-dependent lesion patterns. The importance of geometry was highlighted, and calls into question how accurately it is captured. -
@phdthesis{2016:grazia:three-dimensional, author = {Grazia, Daniele De}, title = {Three-dimensional discontinuous spectral/hp element methods for compressible flows}, school = {Imperial College London}, year = {2016}, url = {http://hdl.handle.net/10044/1/40416}, doi = {10.25560/40416}, groups = {thesis} }In this thesis we analyse and develop two high-order schemes which belong to the class of discontinuous spectral/hp element methods focusing on compressible aerodynamic studies and, more specifically, on boundary-layer flows. We investigate the discontinuous Galerkin method and the flux reconstruction approach providing a detailed analysis of the connections between these methods. The connections found enable a better understanding of the broader class of discontinuous spectral/hp element methods. From this perspective it was evident that some of the issues of the discontinuous Galerkin method are also encountered in the flux reconstruction approach, and in particular, the aliasing errors of the two schemes are identical. The techniques applied in the more famous discontinuous Galerkin method for tackling these errors can be also extended to the flux reconstruction approach. We present two dealiasing strategies based on the concept of consistent integration of the nonlinear terms. The first is a localised approach which targets in each element the nonlinearities arising in the problem, while the second is a more global approach which involves a higher quadrature of the overall right-hand side of the discretised equation(s). Both the strategies have been observed to be effective in enhancing the robustness of the schemes considered. We finally present the direct numerical simulation of a high-speed subsonic boundary-layer flow past a three-dimensional roughness element, achieved by means of the compressible aerodynamic solver developed. This type of analyses have been widely performed in the past with approximated theories. Only recently, has DNS been used due to the improvement of numerical techniques and an increase in computational resources for similar studies in low-speed subsonic, supersonic and hypersonic regimes. This thesis takes a first step to close the gap between the results for a high-speed subsonic regime and the results in supersonic and hypersonic regimes. -
@phdthesis{2016:ekelschot:mesh, author = {Ekelschot, Dirk}, title = {Mesh adaptation strategies for compressible flows using a high-order spectral/hp element discretisation}, school = {Imperial College London}, year = {2016}, url = {http://hdl.handle.net/10044/1/43340}, doi = {10.25560/43340}, groups = {thesis} }An accurate calculation of aerodynamic force coe cients for a given geometry is of fundamental importance for aircraft design. High-order spectral/hp element methods, which use a discontinuous Galerkin discretisation of the compressible Navier-Stokes equations, are now increasingly being used to improve the accuracy of flow simulations and thus the force coe cients. To reduce error in the calculated force coe cients whilst keeping computational cost minimal, I propose a p-adaptation method where the degree of the approximating polynomial is locally increased in the regions of the flow where low resolution is identified using a goal-based error estimator. We initially calculate a steady-state solution to the governing equations using a low polynomial order and use a goal-based error indicator to identify parts of the computational domain that require improved solution accuracy and increase the approximation order there. We demonstrate the cost-effectiveness of our method across a range of polynomial orders by considering a number of examples in two- and three-dimensions and in subsonic and transonic flow regimes. Reductions in both the number of degrees of freedom required to resolve the force coe cients to a given error, as well as the computational cost, are both observed in using the p-adaptive technique. In addition to the adjoint-based p-adaptation strategy, I propose a mesh deformation strategy that relies on a thermo-elastic formulation. The thermal-elastic formulation is initially used to control mesh validity. Two mesh quality indicators are proposed and used to illustrate that by heating up (expanding) or cooling down (contracting) the appropriate elements, an improved robustness of the classical mesh deformation strategy is obtained. The idea is extended to perform shock wave r-adaptation (adaptation through redistribution) for high Mach number flows. The mesh deformation strategy keeps the mesh topology unchanged, contracts the elements that cover the shock wave, keeps the number of elements constant and the computation as e cient as the unrefined case. The suitability of r-adaptation for shock waves is illustrated using internal and external compressible flow problems.
2015
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@phdthesis{2015:mengaldo:discontinuous, author = {Mengaldo, Gianmarco}, title = {Discontinuous spectral/hp element methods: development, analysis and applications to compressible flows}, school = {Imperial College London}, year = {2015}, url = {http://hdl.handle.net/10044/1/28678}, doi = {10.25560/28678}, groups = {thesis} }This thesis is concerned with the development and analysis of discontinuous spectral/hp element methods and their applications to compressible aerodynamics with special focus on boundary-layer flows. In this thesis, we provide a detailed analysis on the connections between the discontinuous Galerkin method and the flux reconstruction approach for multidimensional nonlinear systems of conservation laws on irregular meshes (i.e. meshes with deformed and/or curved elements). The results help a better understanding of the broader class of discontinuous spectral/hp element methods and allow the direct applications to the flux reconstruction approach of the existing and more established techniques used in the discontinuous Galerkin community for tackling various issues of this class of schemes, including their aliasing problems. From this perspective, we present two dealiasing strategies based on the concept of consistent integration of the nonlinear terms (also referred to as over-integration of the linear terms). The first is a localised approach and it targets in each element the nonlinearities arising in the problem, while the second is a more global approach which involves a higher quadrature of the overall right-hand side of the discretised equation(s). The two dealiasing strategies have been observed to be effective in enhancing the numerical stability of both schemes, the flux reconstruction and the discontinuous Galerkin approaches. We finally present the direct numerical simulation of a high-speed subsonic flow past a roughness element, achieved by means of the discontinuous spectral/hp element methods developed. These results were successively compared to some data obtained from the asymptotic triple-deck theory. This work, besides demonstrating that the class of schemes analysed and developed is attractive for such aerodynamic problems, also addresses the lack of comparisons between theoretical models and numerical simulations. -
@phdthesis{2015:chooi:experimental, author = {Chooi, Kok Yean}, title = {Experimental and Numerical Investigation of Arterial Wall Mass Transport}, year = {2015}, publisher = {Imperial College London}, url = {http://hdl.handle.net/10044/1/33349}, doi = {10.25560/33349}, groups = {thesis} }The accumulation of plasma macromolecules in the arterial intima is a critical step in atherogenesis. It depends on the balance between influx across the endothelium and efflux across the media. The work presented in this thesis investigated these phenomena. The distribution of ’hotspots’ of high endothelial permeability around aortic branches was mapped in immature and mature rabbits; the pattern of disease at such sites changes with age. The pattern of hotspots of Evan’s Blue dye-labelled albumin uptake was found to change with age. Using statistical techniques that account for spatial autocorrelation and non-linear relations between variables, a significant correlation with the pattern of cholesterol deposition was obtained at both ages. The hotspot patterns did not correlate with patterns of mitosis. The data also showed that the division of transendothelial transport pathways into ’small’ and ’large’ pores may represent an arbitrary division of a continuum of pore sizes. Albumin is smaller than the lipoproteins thought to trigger atherosclerosis. The study was therefore repeated using rhodamine-labelled 2 MDa dextran. In immature animals, the pattern of hotspots for this larger tracer was similar to the pattern for albumin. The mature pattern of dextran uptake differed from the immature one, but it was not the same as that observed for albumin. Further studies investigated transport through the media. As the transport of large molecules occurs predominantly by advection, characterising transmural water flux is important. Ex vivo experimental studies investigated effects of pressure and muscle contraction on hydraulic resistance. Numerical studies based on structural data from the ex vivo experiments were used to characterise the resistance of the media, and the intimal resistance was obtained by subtraction. Intimal and medial resistances in the order 1011 kg/(s.m.m) were found to change in opposite directions with increasing pressure or muscle contraction. The results may assist in understanding and preventing the development of atherosclerosis. -
@phdthesis{2015:bastien:unstable, author = {Bastien, Jordi}, title = {Unstable steady-state solutions and stability analysis of vortex dominated flow}, school = {Imperial College London}, year = {2015}, url = {http://hdl.handle.net/10044/1/31875}, doi = {10.25560/31875}, groups = {thesis} }To compute stability analysis numerically with high accuracy, it is crucial to carefully choose the base flow around which the governing equations will be linearised. The steady-state solution is mathematically appropriate because it is a genuine solution of the fluid motion equations. In this thesis we introduce an encapsulated formulation of the selective frequency damping (SFD) method. The SFD method is an alternative to the method of Newton to obtain unstable equilibria of dynamical systems. In its encapsulated formulation, the SFD method makes use of splitting methods, which means that it can be wrapped around an existing time-stepping code as a black box. This largely simplifies the implementation of a steady-state solver into an already existing unsteady code. However this method has two main limitations: it does not converge for arbitrary control parameters; and when it does, it may take a very long time to reach a steady-state solution. Hence we also present an adaptive algorithm to address these two issues. We show that by evaluating the dominant eigenvalue of a partially converged steady flow, we can select SFD parameters that ensure an optimum convergence of the method. We apply this adaptive method to several classical two-dimensional test cases of computational fluid dynamics and we show that a steady-state solution can be obtained with a very limited (or without any) a priori knowledge of the flow stability properties. Eventually, we study the three-dimensional behaviour of the interaction between two identical co-rotating trailing vortices. We use the SFD method to obtain steady base flows and compute Tri-Global stability analysis. We show that there is a fundamental qualitative difference between the least stable eigenmode observed at Re = 250 and the most unstable eigenmode obtained at Re = 600.
2014
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@phdthesis{2014:rocco:advanced, author = {Rocco, G}, title = {Advanced Instability Methods using Spectral/hp Discretisations and their Applications to Complex Geometries}, school = {Imperial College London}, year = {2014}, url = {http://hdl.handle.net/10044/1/28686}, doi = {10.25560/28686}, groups = {thesis} }Controlling wakes of flows past bluff bodies is a fundamental problem in a wide range of engineering applications. In the present work, we investigate such problems theoretically and numerically using linear stability analysis. We initially consider a flow past a cylinder in a fully developed vortex shedding regime, and we apply sufficiently high spanwise forcing on the surface of the cylinder to stabilise the near-wake. The effects on the aerodynamic forces, the wake topology and the dynamics of the vorticity are investigated using spanwise sinusoidal and Gaussian forcing. Stability analysis of the linearised Navier-Stokes equations is then performed on the fully three-dimensional flow to investigate the role of the spanwise modulation on the absolute instability associated with the von-Karman street. The three-dimensional global modes allows us to detect the regions where the instability acts, and the interactions of the perturbations with the base flow shed light on the most relevant mechanism for the wake stabilisation. Additional relevant information on the design of an efficient control device are provided by receptivity analysis and the structural sensitivities. A similar approach is used to study the stability of a flow through a compressor passage at a Re=138,500. Due to the complexity of both the geometry and dynamics of the flow, a phase-averaging technique is used to generate a globally periodic basic flow, extracting only the organised structures and neglecting all the background unsteadiness. This approach allows us to perform Floquet and transient growth analyses to detect the structure of the global modes and the presence of convective instabilities.
2013
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@phdthesis{2013:bolis:fourier, author = {Bolis, Alessandro}, title = {Fourier Spectral/hp Element Method: Investigation of Time-Stepping and Parallelisation Strategies}, school = {Imperial College London}, year = {2013}, url = {http://hdl.handle.net/10044/1/25140}, doi = {10.25560/25140}, groups = {thesis} }As computer hardware has evolved, the time required to perform numerical simulations has reduced, allowing investigations of a wide range of new problems. This thesis focuses on algorithm optimization, to minimize run-time, when solving the incompressible Navier-Stokes equations. Aspects affecting performance related to the discretisation and algorithm parallelization are investigated in the context of high-order methods. The roles played by numerical approximations and computational strategies are highlighted and it is recognized that a versatile implementation provides additional benefits, allowing an ad-hoc selection of techniques to fit the needs of heterogeneous computing environments. We initially describe the building blocks of a spectral/hp element and pure spectral method and how they can be encapsulated and combined to create a 3D discretisation, the Fourier spectral/hp element method. Time-stepping strategies are also described and encapsulated in a flexible framework based on the General Linear Method. After implementing and validating an incompressible Navier-Stokes solver, two canonical turbulent flows are analyzed. Afterward a 2D hyperbolic equation is considered to investigate the efficiency of low- and high-order methods when discretising the spatial and temporal derivatives. We perform parametric studies, monitoring accuracy and CPU-time for different numerical approximations. We identify optimal discretisations, demonstrating that high-order methods are the computationally fastest approach to attain a desired accuracy for this problem. Following the same philosophy, we investigate the benefits of using a hybrid parallel implementation. The message passing model is introduced to parallelize different kernels of an incompressible Navier-Stokes solver. Monitoring the parallel performance of these strategies the most efficient approach is highlighted. We also demonstrate that hybrid parallel solutions can be used to significantly extend the strong scalability limit and support greater parallelism.
2012
- V. P.-A. PeifferBiBTeX AbstractStudy of the relation between blood flow and the age-dependent localisation of early atherosclerosisPhD thesis, Imperial College London, 2012. doi 10.25560/14686
@phdthesis{2012:peiffer:study, author = {Peiffer, Veronique Paule-Alberte}, title = {Study of the relation between blood flow and the age-dependent localisation of early atherosclerosis}, school = {Imperial College London}, year = {2012}, url = {http://hdl.handle.net/10044/1/14686}, doi = {10.25560/14686}, groups = {thesis} }Atherosclerosis develops non-uniformly within the arterial system and the distribution of lesions has been observed to change with age. This thesis investigates the concept that the patchiness of the disease is related to local variations in blood flow. Based on the insights from a systematic literature review, a novel study was designed to analyse the relation between haemodynamic factors and age-dependent atherogenesis in the thoracic aorta of rabbits. Arterial geometries were reconstructed by micro-Computed Tomography of vascular corrosion casts, with particular attention to the anatomical accuracy of the dataset. Blood flow was simulated in these geometries using a spectral/hp element method. Distributions of traditional shear-related metrics were calculated and both qualitatively and quantitatively compared to maps of lesion prevalence. In addition, a time-averaged transverse wall shear stress was introduced. A geometric analysis of the dataset of rabbit thoracic aortas revealed a significant change with age in the degree of aortic taper. The geometric changes could explain age-related differences in flow characteristics, in particular in the extent of Dean-type vortical structures into the descending aorta and the strength of a dorsal streak of high shear. The comparative analysis of shear and lesion distributions did not unequivocally support the theory that lesions occur in regions of low shear. The novel haemodynamic metric, in combination with current metrics, enabled an improved identification of zones of multi-directional disturbed flow. In conclusion, this thesis adds to the understanding of the relation between blood flow and early atherosclerosis, and provides tools for use in future studies.
2011
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@phdthesis{2011:vos:from, author = {Vos, Peter}, title = {From h to p efficiently: Optimising the implementation of spectral/hp element methods}, school = {Imperial College London}, year = {2011}, url = {http://hdl.handle.net/10044/1/77143}, doi = {10.25560/77143}, groups = {thesis} }Various aspects that may help to enhance the implementation of the spectral/hp element method have been considered. A first challenge encountered is to implement the method and the corresponding algorithms in a digestible, generic and coherent manner. Therefore, we first of all demonstrate how the mathematical structure of a spectral/ hp element discretisation can be encapsulated in an object-oriented environment, leading to a generic and flexible spectral/hp software library. Secondly, we present a generic framework for time-stepping partial differential equations. Based upon the unifying concept of General Linear Methods, we have designed an object-oriented framework that allows the user to apply a broad range of time-stepping schemes in a unified fashion. The spectral/hp element method can be considered as bridging the gap between the - traditionally low-order - finite element method on one side and spectral methods on the other side. Consequently, a second challenge which arises in implementing the spectral/hp element methods is to design algorithms that perform efficiently for both low- and high-order spectral/hp discretisations, as well as discretisations in the intermediate regime. In this thesis, we describe how the judicious use of different implementation strategies for the evaluation of spectral/hp operators can be employed to achieve high efficiency across a wide range of polynomial orders. Furthermore, we explain how the multi-level static condensation technique can be applied as an efficient direct solution technique for solving linear systems that arise in the spectral/hp element method. Finally, based upon such an efficient implementation of the spectral/hp element method, we analyse which spectral/hp discretisation (that is, which specific combination of mesh size h and polynomial order P) minimises the computational cost to solve an elliptic problem up to a predefined level of accuracy. We investigate this question for a set of both smooth and non-smooth problems. - J. HoesslerPhD thesis, Imperial College London, 2011.BiBTeX
@phdthesis{2011:hoessler:direct, author = {Hoessler, Julien}, title = {Direct numerical simulations and stability analysis of vortex-dominated flows around complex geometries}, school = {Imperial College London}, year = {2011}, url = {http://hdl.handle.net/10044/1/39386}, groups = {thesis} } -
@phdthesis{2011:biotto:discontinuous, author = {Biotto, Cristian}, title = {A discontinuous Galerkin method for the solution of compressible flows}, school = {Imperial College London}, year = {2011}, url = {http://hdl.handle.net/10044/1/6413}, doi = {10.25560/6413}, groups = {thesis} }This thesis presents a methodology for the numerical solution of one-dimensional (1D) and two-dimensional (2D) compressible flows via a discontinuous Galerkin (DG) formulation. The 1D Euler equations are used to assess the performance and stability of the discretisation. The explicit time restriction is derived and it is established that the optimal polynomial degree, p, in terms of efficiency and accuracy of the simulation is p = 5. Since the method is characterised by minimal diffusion, it is particularly well suited for the simulation of the pressure wave generated by train entering a tunnel. A novel treatment of the area-averaged Euler equations is proposed to eliminate oscillations generated by the projection of a moving area on a fixed mesh and the computational results are validated against experimental data. Attention is then focussed on the development of a 2D DG method implemented using the high-order library Nektar++. An Euler and a laminar Navier Stokes solvers are presented and benchmark tests are used to assess their accuracy and performance. An artificial diffusion term is implemented to stabilise the solution of the Euler equations in transonic flow with discontinuities. To speed up the convergence of the explicit method, a new automatic polynomial adaptive procedure (p-adaption) and a new zonal solver are proposed. The p-adaptive procedure uses a discontinuity sensor, originally developed as an artificial diffusion sensor, to assign appropriate polynomial degrees to each element of the domain. The zonal solver uses a modification of a method for matching viscous subdomains to set the interface conditions between viscous and inviscid subdomains that ensures stability of the flow computation. Both the p-adaption and the zonal solver maintain the high-order accuracy of the DG method while reducing the computational cost of the simulation.