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
- 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. - 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 AbstractNektar++: 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} }Nektar++ 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 \pi/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. 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
- 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} }he 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.q
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.
2024
- 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.
2023
- 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. - 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\leq0.16, the 3-D transition is dominated by the LEV-TEV interaction. For 0.16
2022
- 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
- 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 \times 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
- 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. 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
- 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, 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 spectral/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. - 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. - 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.
PhD theses
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: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. - A. CassinelliBiBTeX AbstractA spectral/hp element DNS study of flow past low-pressure turbine cascades and the effects of inflow conditionsPhD thesis, Imperial College London, 2021. doi 10.25560/103146
@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}, 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.
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.