@article{ducros1999large,
  title={Large-eddy simulation of the shock/turbulence interaction},
  author={Ducros, F and Ferrand, V and Nicoud, Franck and Weber, C and Darracq, D and Gacherieu, C and Poinsot, Thierry},
  journal={Journal of Computational Physics},
  volume={152},
  number={2},
  pages={517--549},
  year={1999},
  publisher={Elsevier}
}


@inproceedings{persson2006sub,
  title={Sub-cell shock capturing for {D}iscontinuous {G}alerkin methods},
  author={Persson, P.-O. and Peraire, J.},
  booktitle={44th AIAA Aerospace Sciences Meeting and Exhibit},
  pages={112},
  year={2006}
}

@inbook{MenDeG14,
	Annote = {doi:10.2514/6.2014-2923},
	Author = {Gianmarco Mengaldo and Daniele De Grazia and Freddie Witherden and Antony Farrington and Peter Vincent and Spencer Sherwin and Joaquim Peiro},
	Booktitle = {7th AIAA Theoretical Fluid Mechanics Conference},
	Date-Added = {2014-08-10 14:59:03 +0000},
	Date-Modified = {2014-08-10 14:59:20 +0000},
	Doi = {doi:10.2514/6.2014-2923},
	M1 = {0},
	M3 = {doi:10.2514/6.2014-2923},
	Month = {2014/08/10},
	Publisher = {American Institute of Aeronautics and Astronautics},
	Title = {A Guide to the Implementation of Boundary Conditions in Compact High-Order Methods for Compressible Aerodynamics},
	Title1 = {AIAA Aviation},
	Ty = {CHAP},
	Url = {http://dx.doi.org/10.2514/6.2014-2923},
	Year = {2014},
	Year1 = {2014/06/13},
	Bdsk-Url-1 = {http://dx.doi.org/10.2514/6.2014-2923}}

@article{DeGMen14,
	Author = {De Grazia, D. and Mengaldo, G. and Moxey, D. and Vincent, P. E. and Sherwin, S. J.},
	Date-Added = {2014-08-10 14:57:35 +0000},
	Date-Modified = {2014-08-10 14:58:04 +0000},
	Doi = {10.1002/fld.3915},
	Issn = {1097-0363},
	Journal = {International Journal for Numerical Methods in Fluids},
	Keywords = {flux reconstruction, spectral/hp element methods, discontinuous Galerkin, tensor-product grids, collocation},
	Number = {12},
	Pages = {860--877},
	Title = {Connections between the discontinuous Galerkin method and high-order flux reconstruction schemes},
	Url = {http://dx.doi.org/10.1002/fld.3915},
	Volume = {75},
	Year = {2014},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/fld.3915}}

@book{Toro09,
	Author = {E.F. Toro},
	Date-Added = {2014-08-10 14:25:57 +0000},
	Date-Modified = {2014-08-10 14:28:06 +0000},
	Publisher = {Springer},
	Title = {Riemann Solvers and Numerical methods for Fluid Dynamics, 3rd edition},
	Year = {2009}}

@misc{nektar-website,
	Title = {Nektar++: Spectral/hp element framework},
	Url = {http://www.nektar.info},
	Year = 2014,
	Bdsk-Url-1 = {http://www.nektar.info}}

@article{VoShKi10,
	Author = {Vos, Peter EJ and Sherwin, Spencer J and Kirby, Robert M},
	Journal = {Journal of Computational Physics},
	Number = 13,
	Pages = {5161--5181},
	Publisher = {Elsevier},
	Title = {From h to p efficiently: Implementing finite and spectral/hp element methods to achieve optimal performance for low-and high-order discretisations},
	Volume = 229,
	Year = 2010}

@article{CaShKiKe11b,
	Author = {Cantwell, C. D. and Sherwin, S. J. and Kirby, R. M. and Kelly, P. H. J.},
	Issue = 3,
	Journal = {Math. Mod. Nat. Phenom.},
	Pages = {84--96},
	Title = {From h to p efficiently: selecting the optimal spectral/hp discretisation in three dimensions},
	Volume = 6,
	Year = 2011}

@article{CaShKiKe11a,
	Author = {Cantwell, C. D. and Sherwin, S. J. and Kirby, R. M. and Kelly, P. H. J.},
	Journal = {Computers \& Fluids},
	Pages = {23--28},
	Title = {From h to p efficiently: strategy selection for operator evaluation on hexahedral and tetrahedral elements.},
	Volume = {43},
	Year = {2011}}

@article{AlPa96,
    author = {R. R. Aliev and A. V. Panfilov},
    title = {A simple two-variable model of cardiac excitation},
    journal = {Chaos, Solitons \& Fractals},
    volume = {7},
    issue = {3},
    pages = {293-301},
    year = {1996},
}

@article{CoRaNa98,
    author = {M. Courtemanche\, R. J. Ramirez and S. Nattel},
    title = {Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model},
    journal = {American Journal of Physiology-Heart and Circulatory Physiology},
    volume = {275},
    issue = {1},
    pages = {H301-H321},
    year = {1998},
}

@article{LuRu91,
    author = {C. H. Luo and Y. Rudy},
    title = {A model of the ventricular cardiac action potential. Depolarization\, repolarization\, and their interaction},
    journal = {Circulation research},
    volume = {68},
    issue = {6},
    pages = {1501-1526},
    year = {1991},
}

@article{TuPa06,
    author = {K. H. W. J. ten Tusscher and A. V. Panfilov},
    title = {Alternans and spiral breakup in a human ventricular tissue model},
    journal = {American Journal of Physiology-Heart and Circulatory Physiology},
    volume = {291},
    issue = {3},
    pages = {H1088-H1100},
    year = {2006},
}

@article{NiKeBeBeBe11,
    author = {Niederer ''et al.''},
    title = {Verification of cardiac tissue electrophysiology simulators using an N-version benchmark},
    journal = {Philos Transact A Math Phys Eng Sci},
    volume = {369},
    issue = {1954},
    pages = {4331-51},
    year = {2011},
    }

@article{ShKa96,
  title={Tetrahedral< i> hp</i> Finite Elements: Algorithms and Flow Simulations},
  author={Sherwin, SJ and Karniadakis, G Em},
  journal={Journal of Computational Physics},
  volume={124},
  number={1},
  pages={14--45},
  year={1996},
  publisher={Elsevier}
}

@article{HeWa02,
  title={Nodal high-order methods on unstructured grids: I. Time-domain solution of Maxwell's equations},
  author={Hesthaven, Jan S and Warburton, Tim},
  journal={Journal of Computational Physics},
  volume={181},
  number={1},
  pages={186--221},
  year={2002},
  publisher={Elsevier}
}

@article{BeReCoLeHi09,
  title={High-order discontinuous Galerkin schemes on general 2D manifolds applied to the shallow water equations},
  author={Bernard, P-E and Remacle, J-F and Comblen, Richard and Legat, Vincent and Hillewaert, Koen},
  journal={Journal of Computational Physics},
  volume={228},
  number={17},
  pages={6514--6535},
  year={2009},
  publisher={Elsevier}
}

@book{ZiTa89,
  title={Basic formulation and linear problems},
  author={Zienkiewicz, Olgierd Cecil and Taylor, Robert Leroy},
  year={1989},
  publisher={McGraw-Hill}
}

@book{GoOr77,
  title={Numerical analysis of spectral methods},
  author={Gottlieb, David and Orszag, Steven A and MA, CAMBRIDGE HYDRODYNAMICS INC},
  year={1977},
  publisher={SIAM}
}

@article{BaSu94,
  title={The p and h-p versions of the finite element method, basic principles and properties},
  author={Babu{\v{s}}ka, Ivo and Suri, Manil},
  journal={SIAM review},
  volume={36},
  number={4},
  pages={578--632},
  year={1994},
  publisher={SIAM}
}

@article{Pa84,
  title={A spectral element method for fluid dynamics: laminar flow in a channel expansion},
  author={Patera, Anthony T},
  journal={Journal of computational Physics},
  volume={54},
  number={3},
  pages={468--488},
  year={1984},
  publisher={Elsevier}
}

@article{DoFf83,
    author={Dowling, AP and Ffowcs-Williams JE},
    title={Sound and sources of sound},
    journal={Ellis Horwood series in engineering science},
    year=1983
}

@article{ShFoPeFr03,
    author={Sherwin, SJ and Formaggia, L and Peiró, J and Franke, V},
    title={Computational modelling of 1D blood flow with variable
mechanical properties and its application to the simulation of wave propagation
in the human arterial system},
    journal={Int. J. Numer. Meth. Fluids},
    volume={43},
    pages={673-700},
    year={2003}
}

@article{JoCoSh14,
    author={Jordi, B. E. and Cotter, C. J. and Sherwin, S. J.},
    title={Encapsulated formulation of the selective frequency damping method},
    journal={Phys. Fluids},
    year={2014}
}

@article{MoHaPeSh14,
  title        = {{An isoparametric approach to high-order curvilinear
                  boundary-layer meshing}},
  author       = {Moxey, D. and Hazan, M. and Peir\'o, J. and Sherwin, S. J.},
  year         = 2014,
  doi          = {10.1016/j.cma.2014.09.019},
  journal      = {Comp. Meth. Appl. Mech. Eng.}
}

@unpublished{MoHaPeSh14b,
  title        = {{On the generation of curvilinear meshes through subdivision
                  of isoparametric elements}},
  author       = "D. Moxey and M. Hazan and J. Peir\'o and S. J. Sherwin",
  note         = "to appear in proceedings of Tetrahedron IV",
  year         = 2014
}

@article{We69,
    author={Westerhof, N},
    title={Anatomic studies of the human systemic arterial tree},
    journal={J. Biomech.},
    volume={2},
    pages={121-143},
    year={1969}
}

@thesis{Ro12,
    author={Roth, CJ},
    title={Pulse Wave Propagation in the Human Vascular System},
    type={Diploma Thesis},
    year={2012}
}

@thesis{Pi12,
    author={Pignier, N},
    title={One-dimensional modelling of blood flow in the cardiovascular system},
    type={MSc Project},
    year={2012}
}

@article{NeKa97,
  title={A direct numerical simulation study of flow past a freely vibrating cable},
  author={Newman, David J and Karniadakis, George Em},
  journal={Journal of Fluid Mechanics},
  volume={344},
  pages={95--136},
  year={1997},
  publisher={Cambridge Univ Press}
}

@book{KaSh05,
title={Spectral/hp Element Methods for Computational Fluid Dynamics},
author={Karniadakis, G. E. and Sherwin, S. J.},
publisher={Oxford Science Publications},
year={2005}
}

@article{Bu06,
title={General linear methods},
author={Butcher, J. C.},
journal={Acta Numerica},
volume={15},
pages={157-256},
year={2006}
}

@article{VoEsBoChKi11,
title={A generic framework for time-stepping partial differential equations (PDEs):
general linear methods, object-oriented implementation and application to fluid
problems},
author={Vos, P. E. J. and Eskilsson, C. and Bolis, A. and Chun, S. and Kirby, R. M.
and Sherwin, S. J.},
journal={International Journal of Computational Fluid Dynamics},
volume={25},
issue={3},
pages={107-125},
year={2011}
}

@article{CaMoCoBoRo15,
  title={Nektar++: An open-source spectral/hp element framework},
  author={Cantwell, CD and Moxey, D and Comerford, A and Bolis, A and Rocco, G and Mengaldo, G and De Grazia, D and Yakovlev, S and Lombard, J-E and Ekelschot, D and others},
  journal={Computer Physics Communications},
  volume={192},
  year={2015},
  pages={205-219},
  publisher={Elsevier}
}

@book{Ga39,
  title={Orthogonal polynomials},
  author={Gabor Szeg{\"o}},
  volume={23},
  year={1939},
  publisher={American Mathematical Soc.}
}

@book{AbSt64,
  title={Handbook of mathematical functions},
  author={Abramowitz, Milton and Stegun, Irene A},
  year={1972},
  publisher={Dover}
}

@techreport{CaHuYoQu88,
  title={Spectral methods in fluid dynamics},
  author={Canuto, Claudio and Hussaini, M Yousuff and Quarteroni, Alfio and Zang, Thomas A},
  year={1988},
  institution={Springer}
}

@article{GhOs70,
  title={Quadrature formulae},
  author={Ghizzetti, Alessandro and Ossicini, Aldo},
  year={1970},
  publisher={Birkh{\"a}user}
}
@article{DoKa14,
  title={A robust and accurate outflow boundary condition for incompressible
        flow simulations on severely-truncated unbounded domains},
  author={S. Dong and G. E. Karniadakis and C. Chryssostomidis},
  journal={Journal of Computational Physics},
  volume={261},
  pages={95--136},
  year={2014}
}


@article{Dong15,
  title={A convective-like energy-stable open boundary condition for simulation of incompressible flows},
  author={S. Dong},
  journal={Journal of Computational Physics},
  volume={302},
  pages={300-328},
  year={2015}
}

@article{Ko07,
  title        = {Vectorized Matlab codes for linear two-dimensional elasticity},
  author       = {Koko, Jonas},
  journal      = {Scientific Programming},
  volume       = 15,
  number       = 3,
  pages        = {157--172},
  year         = 2007,
  publisher    = {IOS Press}
}

@Article{KaIsOr91,
  author = 	 "G. E. Karniadakis and M. Israeli and S. A. Orszag",
  title = 	 "High-order splitting methods for the incompressible
		  {Navier}--{Stokes} equations",
  journal =	 JCP,
  year =	 1991,
  volume =	 97,
  number =	 2,
  pages =	 "414--443"
}

@article{GuSh03,
  Author="J.L. Guermond and J. Shen",
  title="Velocity-correction projection methods for incompressible flows",
  journal="SIAM J. Numer.\ Anal.",
  volume=41,
  pages = "112--134",
  year=2003
}

@article{XiShDoKa,
  author = {Xiu, D and Sherwin, SJ and Dong, S and Karniadakis, GE},
  doi = {10.1007/s10915-004-4647-1},
  journal = {J. Sci. Comp. },
  pages = {323--346},
  title = {Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows},
  url = {http://dx.doi.org/10.1007/s10915-004-4647-1},
  volume = {25},
  year = {2005}
}

@inproceedings{Sh03,
  author = {Sherwin, S},
  pages = {43--52},
  publisher = {Elsevier Science},
  title = {A substepping Navier-Stokes splitting scheme for spectral/hp element discretisations},
  url = {http://www2.imperial.ac.uk/ssherw/spectralhp/papers/Conferences/pcfd_sherwin.pdf},
  year = {2003}
}

@Article{MaPaRo,
  author =       {Y. Maday and A. T. Patera and E.M. Ronquist},
  title =        {An operator-integration-factor splitting method for time-dependent problems: Application to incompressible fludi flow},
  journal =      {J. Sci. Comp.},
  year =         {1990},
  volume =       {4},
  pages =        {263-292},
}


@article{AiSh,
  author = {Ainsworth, M and Sherwin, S},
  doi = {10.1016/S0045-7825(98)00356-9},
  journal = {COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING},
  pages = {243--266},
  title = {Domain decomposition preconditioners for p and hp finite element approximation of Stokes equations},
  url = {http://dx.doi.org/10.1016/S0045-7825(98)00356-9},
  volume = {175},
  year = {1999}
}

@article{ShAi,
  author = {Sherwin, SJ and Ainsworth, M},
  doi = {10.1016/S0168-9274(99)00102-6},
  journal = {APPLIED NUMERICAL MATHEMATICS},
  pages = {357--363},
  title = {Unsteady Navier-Stokes solvers using hybrid spectral/hp element methods},
  url = {http://dx.doi.org/10.1016/S0168-9274(99)00102-6},
  volume = {33},
  year = {2000}
}

@article{GaRoPeSa15,
  title        = {Distortion and quality measures for validating and generating
                  high-order tetrahedral meshes},
  author       = {Gargallo-Peir{\'o}, Abel and Roca, Xevi and Peraire, Jaime and
                  Sarrate, Josep},
  journal      = {Engineering with Computers},
  volume       = 31,
  number       = 3,
  pages        = {423--437},
  year         = 2015,
  publisher    = {Springer London}
}

@Article{BaPlGrSh16,
  author =       {Bao, Y.  and Palacios, R. and Graham, M. and Sherwin, S.J. },
  title =        {Generalized “thick” strip modelling for vortex-induced vibration of long flexible cylinders},
  journal =      {J. Comp. Phys},
  year =         {2016},
  volume =       {321},
  pages =        {1079-1097},
}

@inproceedings{TuPeMo16,
abstract = {The generation of sufficiently high quality unstructured high-order meshes remains a significant obstacle in the adoption of high-order methods. However, there is little consensus on which approach is the most robust, fastest and produces the 'best' meshes. We aim to provide a route to investigate this question, by examining popular high-order mesh generation methods in the context of an efficient variational framework for the generation of curvilinear meshes. By considering previous works in a variational form, we are able to compare their characteristics and study their robustness. Alongside a description of the theory and practical implementation details, including an efficient multi-threading parallelisation strategy, we demonstrate the effectiveness of the framework, showing how it can be used for both mesh quality optimisation and untangling of invalid meshes.},
author = {Turner, M and Peir{\'{o}}, J and Moxey, D},
booktitle = {25th International Meshing Roundtable},
doi = {10.1016/j.proeng.2016.11.069},
file = {:Users/mike/Downloads/1-s2.0-S1877705816333781-main.pdf:pdf},
issn = {18777058},
keywords = {energy functional,high-order mesh generation,numerical optimization,variational mesh generation},
pages = {340--352},
title = {{A Variational Framework for High-Order Mesh Generation}},
url = {www.elsevier.com/locate/procedia%5Cnhttp://linkinghub.elsevier.com/retrieve/pii/S1877705816333781},
volume = {163},
year = {2016}
}

@article{rospjo16,
  title={Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection--diffusion problems: Insights into spectral vanishing viscosity},
  author={Moura, RC and Sherwin, SJ and Peir{\'o}, Joaquim},
  journal={Journal of Computational Physics},
  volume={307},
  pages={401--422},
  year={2016},
  publisher={Elsevier}
}

@article{yvsiouei93,
  title={Legendre pseudospectral viscosity method for nonlinear conservation laws},
  author={Maday, Yvon and Kaber, Sidi M Ould and Tadmor, Eitan},
  journal={SIAM Journal on Numerical Analysis},
  volume={30},
  number={2},
  pages={321--342},
  year={1993},
  publisher={SIAM}
}

@article{rosh06,
  title={Stabilisation of spectral/hp element methods through spectral vanishing viscosity: Application to fluid mechanics modelling},
  author={Kirby, Robert M and Sherwin, Spencer J},
  journal={Computer methods in applied mechanics and engineering},
  volume={195},
  number={23},
  pages={3128--3144},
  year={2006},
  publisher={Elsevier}
}

@article{EwSc03,
    author   = {Ewert, Roland and Schr{\"{o}}der, Wolfgang},
    title    = {{Acoustic perturbation equations based on flow decomposition via source filtering}},
    journal  = {Journal of Computational Physics},
    year     = {2003},
    volume   = {188},
    number   = {2},
    month    = {7},
    pages    = {365--398},
    issn     = {00219991},
    doi      = {10.1016/S0021-9991(03)00168-2},
    url      = {http://linkinghub.elsevier.com/retrieve/pii/S0021999103001682},
    keywords = {APE,acoustic perturbation equations,caa,flow decomposition,les,source filtering},
}

@InProceedings{Ge14,
    author    = {Geiser, Georg and Nawroth, Holger and Hosseinzadeh, Arash and Zhang, Feichi and Bockhorn, Henning and Habisreuther, Peter and Janicka, Johannes and Paschereit, Christian O. and Schröder, Wolfgang},
    title     = {Thermoacoustics of a turbulent premixed flame},
    booktitle = {20th AIAA/CEAS Aeroacoustics Conference},
    date      = {2014-06},
    publisher = {American Institute of Aeronautics and Astronautics},
    doi       = {10.2514/6.2014-2476},
}

@phdthesis{La18,
    author = {Lackhove, Kilian},
    title  = {{Hybrid Noise Simulation for Enclosed Configurations}},
    year   = {2018},
    type   = {Doctoral Thesis},
    school = {Technische Universität Darmstadt},
    url    = {http://tuprints.ulb.tu-darmstadt.de/id/eprint/7611},
}

@article{NakayamaSPM,
  title = {Simulation method to resolve hydrodynamic interactions in colloidal dispersions},
  author = {Nakayama, Yasuya and Yamamoto, Ryoichi},
  journal = {Phys. Rev. E},
  volume = {71},
  issue = {3},
  pages = {036707},
  numpages = {7},
  year = {2005},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevE.71.036707},
  url = {https://link.aps.org/doi/10.1103/PhysRevE.71.036707}
}

@article{LuoSPM,
    abstract = {We re-formulate and analyze a new method for particulate flows, the so-called ``smoothed profile'' method (SPM) first proposed in [Y. Nakayama, R. Yamamoto, Simulation method to resolve hydrodynamic interactions in colloidal dispersions, Phys. Rev. E 71 (2005) 036707], which uses a fixed computational mesh without conformation to the geometry of the particles. The method represents the particles by certain smoothed profiles to construct a body force term added into the Navier--Stokes equations. SPM imposes accurately and efficiently the proper conditions at the particle--fluid interface. In particular, while the original method employs a fully-explicit time-integration scheme we develop a high-order semi-implicit splitting scheme, which we implement in the context of spectral/hp element discretization. First, we show that the modeling error of SPM has a non-monotonic dependence on the time step size \ensuremath{\Delta}t; it is a function of \ensuremath{\nu}\ensuremath{\Delta}t/\ensuremath{\xi}, where \ensuremath{\nu} is the kinematic viscosity of fluid and \ensuremath{\xi} is the interface thickness of the smoothed profile. Subsequently, we present several steady and unsteady simulations, including flow past 3D complex-shaped particles, and compare against direct numerical simulations and the force coupling method (FCM).},
    author = {Luo, Xian and Maxey, Martin R. and Karniadakis, George Em},
    doi = {10.1016/j.jcp.2008.11.006},
    issn = {0021-9991},
    journal = {Journal of Computational Physics},
    keywords = {SPM, Two-phase flow, Suspensions, Time-splitting scheme},
    number = {5},
    pages = {1750--1769},
    title = {{Smoothed profile method for particulate flows: Error analysis and simulations}},
    url = {http://www.sciencedirect.com/science/article/pii/S0021999108005925},
    volume = {228},
    year = {2009}
}

@article{WangSPM,
    abstract = {An accurate, fast and robust spectral-element/Fourier smoothed profile method (SEF-SPM) for turbulent flow past 3D complex-geometry moving bluff-bodies is developed and analyzed in this paper. Based on the concept of momentum thickness \ensuremath{\delta}2, a new formula for determining the interface thickness parameter \ensuremath{\xi} is proposed. In order to overcome the numerical instability at high Reynolds number, the so-called Entropy Viscosity Method (EVM) is introduced in the framework of large-eddy simulation. To overcome resolution constraints pertaining to moving immersed bodies, the Coordinate Transformation Method (Mapping method) is incorporated in the current implementation. Moreover, a hybrid spectral-element method using mixed triangular and quadrilateral elements is employed in conjunction with Fourier discretization along the third direction to efficiently represent a body of revolution or a long-aspect ratio bluff-body like risers and cables. The combination of the above algorithms results in a robust method which we validate by several prototype flows, including flow past a stationary sphere at 200 \ensuremath{\leq} Re \ensuremath{\leq} 1000, as well as turbulent flow past a stationary and moving cylinder at 80 \ensuremath{\leq} Re \ensuremath{\leq} 10, 000. Finally, we apply the new method to simulate a self-excited rigidly moving dual-step cylinder and demonstrate that SEF-SPM is an efficient method for complex VIV problems.},
    author = {Wang, Zhicheng and Triantafyllou, Michael S and Constantinides, Yiannis and Karniadakis, George Em},
    doi = {10.1016/j.compfluid.2018.06.022},
    issn = {0045-7930},
    journal = {Computers \& Fluids},
    keywords = {High-order methods, LES, Entropy-viscosity, Hybrid discretization, Industrial flows},
    pages = {84--96},
    title = {{A spectral-element/Fourier smoothed profile method for large-eddy simulations of complex VIV problems}},
    url = {http://www.sciencedirect.com/science/article/pii/S0045793018303529},
    volume = {172},
    year = {2018}
}

@article{FISCHER1998193,
	title = "Projection techniques for iterative solution of Ax = b with successive right-hand sides",
	journal = "Computer Methods in Applied Mechanics and Engineering",
	volume = "163",
	number = "1",
	pages = "193 - 204",
	year = "1998",
	issn = "0045-7825",
	doi = "https://doi.org/10.1016/S0045-7825(98)00012-7",
	url = "http://www.sciencedirect.com/science/article/pii/S0045782598000127",
	author = "Paul F. Fischer",
	abstract = "Projection techniques are developed for computing approximate solutions to linear systems of the form Axn = bn, for a sequence n = 1, 2,…, e.g. arising from time discretization of a partial differential equation. The approximate solutions are based upon previous solutions, and can be used as initial guesses for iterative solution of the system, resulting in significantly reduced computational expense. Examples of two- and three-dimensional incompressible Navier-Stokes calculations are presented in which xn represents the pressure at time level tn, and A is a consistent discrete Poisson operator. In flows containing significant dynamic activity, these projection techniques lead to as much as a two-fold reduction in solution time."
}

@article{moura2022gradient,
  title={Gradient jump penalty stabilisation of spectral/hp element discretisation for under-resolved turbulence simulations},
  author={Moura, Rodrigo C and Cassinelli, Andrea and da Silva, Andr{\'e} FC and Burman, Erik and Sherwin, Spencer J},
  journal={Computer Methods in Applied Mechanics and Engineering},
  volume={388},
  pages={114200},
  year={2022},
  publisher={Elsevier}
}

@article{Dong2010,
  author       = {S. Dong and J. Shen},
  date         = {2010},
  journaltitle = {Journal of Computational Physics},
  title        = {An unconditionally stable rotational velocity-correction scheme for incompressible flows},
  doi          = {10.1016/j.jcp.2010.05.037},
  issn         = {0021-9991},
  number       = {19},
  pages        = {7013-7029},
  url          = {https://www.sciencedirect.com/science/article/pii/S0021999110002986},
  volume       = {229},
  abstract     = {We present an unconditionally stable splitting scheme for incompressible Navier–Stokes equations based on the rotational velocity-correction formulation. The main advantages of the scheme are: (i) it allows the use of time step sizes considerably larger than the widely-used semi-implicit type schemes: the time step size is only constrained by accuracy; (ii) it does not require the velocity and pressure approximation spaces to satisfy the usual inf–sup condition: in particular, the equal-order finite element/spectral element approximation spaces can be used; (iii) it only requires solving a pressure Poisson equation and a linear convection–diffusion equation at each time step. Numerical tests indicate that the computational cost of the new scheme for each time step, under identical time step sizes, is even less expensive than the semi-implicit scheme with low element orders. Therefore, the total computational cost of the new scheme can be significantly less than the usual semi-implicit scheme.},
}

@article{iyer2001,
	title = {An {Experimentalist}’s {Approach} to {Accurate} {Localization} of {Phase} {Singularities} during {Reentry}},
	volume = {29},
	issn = {0090-6964},
	url = {http://link.springer.com/10.1114/1.1335538},
	doi = {10.1114/1.1335538},
	language = {en},
	number = {1},
	urldate = {2020-09-24},
	journal = {Annals of Biomedical Engineering},
	author = {Iyer, Anand N. and Gray, Richard A.},
	month = jan,
	year = {2001},
	pages = {47--59}
}

@article{Simo1994,
  author       = {J. C. Simo and F. Armero},
  date         = {1994},
  journaltitle = {Computer Methods in Applied Mechanics and Engineering},
  title        = {Unconditional stability and long-term behavior of transient algorithms for the incompressible Navier-Stokes and Euler equations},
  doi          = {10.1016/0045-7825(94)90042-6},
  issn         = {0045-7825},
  number       = {1},
  pages        = {111-154},
  url          = {https://www.sciencedirect.com/science/article/pii/0045782594900426},
  volume       = {111},
  abstract     = {This paper examines the long-term behavior, dissipativity and unconditional nonlinear stability properties of time integration algorithms for the incompressible Navier-Stokes equations, including both direct schemes and fractional step/projection methods. The algorithms are termed nonlinear unconditionally stable if, in the absence of a forcing term but for arbitrary initial conditions, the computed kinetic energy decreases for arbitrary step sizes (i.e., L2-stability). Such an a priori stability estimate is a characteristic feature of the Navier-Stokes system. Similarly, the algorithms are said to exhibit asymptotic δt-independent long-term dissipative behavior if, as the continuum flow generated by the Navier-Stokes equations, the algorithmic flow also exhibits an absorbing set (and a maximal attractor). Both direct and fractional step methods are described which inherit these fundamental properties of the Navier-Stokes system for any time step size. Moreover, a subclass of algorithms which retain these strong notions of nonlinear stability and long-term dissipative behavior is identified which, in addition, has the remarkable property of being linear within the time step. The key implication is that no iterations are required to compute the solution within a time step. A specific member of this class is shown to possess the same absorbing set as the continuum Navier-Stokes system. A second order accurate, unconditionally stable method is also identified which retains the property of linearity within a time step. Numerical analysis and computational aspects involved in the implementation of these methods are addressed in detail and illustrated in representative numerical simulations.}
}

@Article{BiGlobal,
author = {D, Barkley and HM, Blackburn and SJ, Sherwin},
doi = {10.1002/fld.1824},
journal = {International Journal for Numerical Methods in Fluids},
pages = {1435--1458},
title = {Direct optimal growth analysis for timesteppers},
url = {http://dx.doi.org/10.1002/fld.1824},
volume = {57},
year = {2008}
}

