Spectral/hp element methods: Recent developments, applications, and perspectives

[1]  Jan S. Hesthaven,et al.  Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction , 2018, J. Comput. Phys..

[2]  Clint Dawson,et al.  An explicit hybridized discontinuous Galerkin method for Serre-Green-Naghdi wave model , 2018 .

[3]  David Moxey,et al.  Towards p-Adaptive Spectral/hp Element Methods for Modelling Industrial Flows , 2017 .

[4]  Spencer J. Sherwin,et al.  Direct numerical simulations of the flow around wings with spanwise waviness , 2017, Journal of Fluid Mechanics.

[5]  Spencer J. Sherwin,et al.  Destabilisation and modification of Tollmien–Schlichting disturbances by a three-dimensional surface indentation , 2017, Journal of Fluid Mechanics.

[6]  Freddie D. Witherden,et al.  On the utility of GPU accelerated high-order methods for unsteady flow simulations: A comparison with industry-standard tools , 2017, J. Comput. Phys..

[7]  Spencer J. Sherwin,et al.  Direct numerical simulations of the flow around wings with spanwise waviness at a very low Reynolds number , 2017 .

[8]  Claes Eskilsson,et al.  Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces , 2017, J. Comput. Phys..

[9]  Spencer J. Sherwin,et al.  A p-adaptation method for compressible flow problems using a goal-based error indicator , 2017 .

[10]  Spencer J. Sherwin,et al.  On the eddy-resolving capability of high-order discontinuous Galerkin approaches to implicit LES / under-resolved DNS of Euler turbulence , 2017, J. Comput. Phys..

[11]  Spencer J. Sherwin,et al.  Influence of localised smooth steps on the instability of a boundary layer , 2015, Journal of Fluid Mechanics.

[12]  Spencer J. Sherwin,et al.  Optimising the performance of the spectral/hp element method with collective linear algebra operations , 2016 .

[13]  Spencer J. Sherwin,et al.  An adaptable parallel algorithm for the direct numerical simulation of incompressible turbulent flows using a Fourier spectral/hp element method and MPI virtual topologies , 2016, Comput. Phys. Commun..

[14]  S. A. Maslowe,et al.  Elliptical instability of the Moore–Saffman model for a trailing wingtip vortex , 2016, Journal of Fluid Mechanics.

[15]  Spencer J. Sherwin,et al.  Velocity-correction schemes for the incompressible Navier-Stokes equations in general coordinate systems , 2016, J. Comput. Phys..

[16]  Claes Eskilsson,et al.  Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation , 2016 .

[17]  Robert Michael Kirby,et al.  To CG or to HDG: A Comparative Study in 3D , 2016, J. Sci. Comput..

[18]  S. Sherwin,et al.  The behaviour of Tollmien–Schlichting waves undergoing small-scale localised distortions , 2016, Journal of Fluid Mechanics.

[19]  Spencer J. Sherwin,et al.  High-order curvilinear meshing using a thermo-elastic analogy , 2016, Comput. Aided Des..

[20]  Spencer J. Sherwin,et al.  Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection-diffusion problems: Insights into spectral vanishing viscosity , 2016, J. Comput. Phys..

[21]  C. Williamson,et al.  Dynamics and Instabilities of Vortex Pairs , 2016 .

[22]  Claes Eskilsson,et al.  A stabilised nodal spectral element method for fully nonlinear water waves , 2015, J. Comput. Phys..

[23]  C. Munz,et al.  A Robust High-Order Discontinuous Galerkin Solver for Fluid Flow with Cavitation , 2016 .

[24]  Spencer J. Sherwin,et al.  Implicit Large-Eddy Simulation of a Wingtip Vortex , 2016 .

[25]  Michael Dumbser,et al.  A space-time discontinuous Galerkin method for Boussinesq-type equations , 2016, Appl. Math. Comput..

[26]  David Moxey,et al.  A Variational Framework for High-order Mesh Generation , 2016 .

[27]  Spencer J. Sherwin,et al.  Dealiasing techniques for high-order spectral element methods on regular and irregular grids , 2015, J. Comput. Phys..

[28]  Spencer J. Sherwin,et al.  Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods , 2015, J. Comput. Phys..

[29]  Bastien Jordi,et al.  Steady-state solvers for stability analysis of vortex dominated flows , 2015 .

[30]  M Nowak,et al.  A combined numerical and experimental framework for determining permeability properties of the arterial media , 2015, Biomechanics and modeling in mechanobiology.

[31]  Robert Michael Kirby,et al.  Nektar++: An open-source spectral/hp element framework , 2015, Comput. Phys. Commun..

[32]  Dan S. Henningson,et al.  Direct numerical simulation of the flow around a wall-mounted square cylinder under various inflow conditions , 2015 .

[33]  S. Sherwin,et al.  An isoparametric approach to high-order curvilinear boundary-layer meshing , 2015 .

[34]  Fabien Marche,et al.  Discontinuous-GalerkinDiscretizationof aNewClass of Green-Naghdi Equations , 2015 .

[35]  Claus-Dieter Munz,et al.  High‐order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations , 2014 .

[36]  Yao Zhang,et al.  Discontinuous Galerkin methods for solving Boussinesq-Green-Naghdi equations in resolving non-linear and dispersive surface water waves , 2014, J. Comput. Phys..

[37]  Lei Bao,et al.  A mass and momentum flux-form high-order discontinuous Galerkin shallow water model on the cubed-sphere , 2014, J. Comput. Phys..

[38]  Robert Michael Kirby,et al.  Exploiting Batch Processing on Streaming Architectures to Solve 2D Elliptic Finite Element Problems: A Hybridized Discontinuous Galerkin (HDG) Case Study , 2013, Journal of Scientific Computing.

[39]  Laslo T. Diosady,et al.  DNS of Flows over Periodic Hills using a Discontinuous-Galerkin Spectral-Element Method , 2014 .

[40]  E. Lamballais,et al.  Evaluation of a high-order discontinuous Galerkin method for the DNS of turbulent flows , 2014 .

[41]  S. Sherwin,et al.  From h to p efficiently: optimal implementation strategies for explicit time-dependent problems using the spectral/hp element method , 2014, International journal for numerical methods in fluids.

[42]  G. Rocco,et al.  Advanced instability methods using spectral/hp discretisations and their applications to complex geometries , 2014 .

[43]  Robert Michael Kirby,et al.  High-order spectral/hp element discretisation for reaction–diffusion problems on surfaces: Application to cardiac electrophysiology , 2014, J. Comput. Phys..

[44]  David Moxey,et al.  23rd International Meshing Roundtable (IMR23) A thermo-elastic analogy for high-order curvilinear meshing with control of mesh validity and quality , 2014 .

[45]  Maurizio Brocchini,et al.  A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics , 2013, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[46]  Rémi Abgrall,et al.  High‐order CFD methods: current status and perspective , 2013 .

[47]  H. Babinsky,et al.  Lift and the leading-edge vortex , 2013, Journal of Fluid Mechanics.

[48]  Dimitri J. Mavriplis,et al.  Discontinuous Galerkin unsteady discrete adjoint method for real-time efficient Tsunami simulations , 2013, J. Comput. Phys..

[49]  Sehun Chun,et al.  Method of Moving Frames to Solve Conservation Laws on Curved Surfaces , 2012, J. Sci. Comput..

[50]  Jörg Stiller,et al.  Adapting the spectral vanishing viscosity method for large-eddy simulations in cylindrical configurations , 2012, J. Comput. Phys..

[51]  Amik St-Cyr,et al.  A Dynamic hp-Adaptive Discontinuous Galerkin Method for Shallow-Water Flows on the Sphere with Application to a Global Tsunami Simulation , 2012 .

[52]  Andrew Pollard,et al.  Direct numerical simulation of compressible turbulent channel flows using the discontinuous Galerkin method , 2011 .

[53]  S. Sherwin,et al.  From h to p efficiently: Strategy selection for operator evaluation on hexahedral and tetrahedral elements , 2011 .

[54]  Spencer J. Sherwin,et al.  A generic framework for time-stepping partial differential equations (PDEs): general linear methods, object-oriented implementation and application to fluid problems , 2011 .

[55]  Dan S. Henningson,et al.  Stabilization of the Spectral-Element Method in Turbulent Flow Simulations , 2011 .

[56]  Spencer J. Sherwin,et al.  From h to p Efficiently: Selecting the Optimal Spectral/hp Discretisation in Three Dimensions , 2011 .

[57]  D. Barkley,et al.  Computational study of subcritical response in flow past a circular cylinder. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[58]  Robert Michael Kirby,et al.  From h to p efficiently: Implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisations , 2010, J. Comput. Phys..

[59]  D. Barkley,et al.  Transient growth analysis of flow through a sudden expansion in a circular pipe , 2010 .

[60]  B. A. P. Reif,et al.  Variational multiscale turbulence modelling in a high order spectral element method , 2006, J. Comput. Phys..

[61]  Christophe Geuzaine,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[62]  Francis X. Giraldo,et al.  A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates , 2008, J. Comput. Phys..

[63]  V.-T. Nguyen,et al.  A discontinuous Galerkin front tracking method for two-phase flows with surface tension , 2008 .

[64]  S. Sherwin,et al.  Direct optimal growth analysis for timesteppers , 2008 .

[65]  S. Sherwin,et al.  Convective instability and transient growth in steady and pulsatile stenotic flows , 2008, Journal of Fluid Mechanics.

[66]  Jan S. Hesthaven,et al.  DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations , 2008 .

[67]  S. Sherwin,et al.  Convective instability and transient growth in flow over a backward-facing step , 2007, Journal of Fluid Mechanics.

[68]  Eric Serre,et al.  A spectral vanishing viscosity for the LES of turbulent flows within rotating cavities , 2007, J. Comput. Phys..

[69]  S. Sherwin,et al.  Comparison of various fluid-structure interaction methods for deformable bodies , 2007 .

[70]  J. Hesthaven,et al.  Nodal DG-FEM solution of high-order Boussinesq-type equations , 2007 .

[71]  Spencer J. Sherwin,et al.  Aliasing errors due to quadratic nonlinearities on triangular spectral /hp element discretisations , 2007 .

[72]  Jean-François Remacle,et al.  A stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows , 2006, J. Comput. Phys..

[73]  Spencer J. Sherwin,et al.  An unstructured spectral/hp element model for enhanced Boussinesq-type equations , 2006 .

[74]  N. Bodard,et al.  Fluid-Structure Interaction by the Spectral Element Method , 2006, J. Sci. Comput..

[75]  Chuanju Xu,et al.  Stabilization Methods for Spectral Element Computations of Incompressible Flows , 2006, J. Sci. Comput..

[76]  Richard Pasquetti,et al.  Spectral Vanishing Viscosity Method for Large-Eddy Simulation of Turbulent Flows , 2006, J. Sci. Comput..

[77]  Roland Bouffanais,et al.  Mesh Update Techniques for Free-Surface Flow Solvers Using Spectral Element Method , 2006, J. Sci. Comput..

[78]  S. Sherwin,et al.  STABILISATION OF SPECTRAL/HP ELEMENT METHODS THROUGH SPECTRAL VANISHING VISCOSITY: APPLICATION TO FLUID MECHANICS MODELLING , 2006 .

[79]  Spencer J. Sherwin,et al.  Spectral/hp discontinuous Galerkin methods for modelling 2D Boussinesq equations , 2006, J. Comput. Phys..

[80]  Q. W. Ma,et al.  Quasi ALE finite element method for nonlinear water waves , 2006, J. Comput. Phys..

[81]  Spencer J. Sherwin,et al.  SPECTRAL ELEMENT STABILITY ANALYSIS OF VORTICAL FLOWS , 2006 .

[82]  J. Hesthaven,et al.  A level set discontinuous Galerkin method for free surface flows , 2006 .

[83]  Taehun Lee,et al.  A level set characteristic Galerkin finite element method for free surface flows , 2005 .

[84]  G. Karniadakis,et al.  Spectral/hp Element Methods for Computational Fluid Dynamics , 2005 .

[85]  Stephen J. Thomas,et al.  A Discontinuous Galerkin Global Shallow Water Model , 2005, Monthly Weather Review.

[86]  R. Pasquetti,et al.  Spectral vanishing viscosity method for LES: sensitivity to the SVV control parameters , 2005 .

[87]  Spencer J. Sherwin,et al.  The next step in coastal numerical models: spectral/hp element methods? , 2005 .

[88]  Spencer J. Sherwin,et al.  Discontinuous Galerkin Spectral/hp Element Modelling of Dispersive Shallow Water Systems , 2005, J. Sci. Comput..

[89]  Michael A. Sprague,et al.  A spectral‐element method for modelling cavitation in transient fluid–structure interaction , 2004 .

[90]  Spencer J. Sherwin,et al.  Formulation of a Galerkin spectral element-fourier method for three-dimensional incompressible flows in cylindrical geometries , 2004 .

[91]  Mark Sussman,et al.  A Discontinuous Spectral Element Method for the Level Set Equation , 2003, J. Sci. Comput..

[92]  George Em Karniadakis,et al.  De-aliasing on non-uniform grids: algorithms and applications , 2003 .

[93]  Hugh Maurice Blackburn,et al.  Spectral element filtering techniques for large eddy simulation with dynamic estimation , 2003 .

[94]  S. Scott Collis,et al.  Discontinuous Galerkin Methods for Compressible DNS , 2003 .

[95]  Michael A. Sprague,et al.  Spectral elements and field separation for an acoustic fluid subject to cavitation , 2003 .

[96]  George Em Karniadakis,et al.  Coarse Resolution Turbulence Simulations With Spectral Vanishing Viscosity—Large-Eddy Simulations (SVV-LES) , 2002 .

[97]  Spencer J. Sherwin,et al.  A Discontinuous Spectral Element Model for Boussinesq-Type Equations , 2002, J. Sci. Comput..

[98]  S. Scott Collis,et al.  Discontinuous Galerkin Methods for Turbulence Simulation , 2002 .

[99]  Jan S. Hesthaven,et al.  Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations , 2002 .

[100]  P. Fischer,et al.  Large eddy simulation of turbulent channel flows by the rational large eddy simulation model , 2002, math/0205264.

[101]  S. Sherwin,et al.  Mesh generation in curvilinear domains using high‐order elements , 2002 .

[102]  Roger E. A. Arndt,et al.  CAVITATION IN VORTICAL FLOWS , 2002 .

[103]  G. Wu,et al.  Finite element simulation of fully non‐linear interaction between vertical cylinders and steep waves. Part 1: methodology and numerical procedure , 2001 .

[104]  Julia S. Mullen,et al.  Filter-based stabilization of spectral element methods , 2001 .

[105]  P. Saugat.  Large eddy simulation for incompressible flows , 2001 .

[106]  George Em Karniadakis,et al.  A Spectral Vanishing Viscosity Method for Large-Eddy Simulations , 2000 .

[107]  S. Orszag,et al.  Numerical investigation of transitional and weak turbulent flow past a sphere , 2000, Journal of Fluid Mechanics.

[108]  Spencer J. Sherwin,et al.  Regular Article: Free-Surface Flow Simulation Using hp/Spectral Elements , 1999 .

[109]  Sailkat Dey,et al.  Curvilinear Mesh Generation in 3D , 1999, IMR.

[110]  Xing Cai,et al.  A Finite Element Method for Fully Nonlinear Water Waves , 1998 .

[111]  Paul Fischer,et al.  An Overlapping Schwarz Method for Spectral Element Solution of the Incompressible Navier-Stokes Equations , 1997 .

[112]  M. Taylor.  The Spectral Element Method for the Shallow Water Equations on the Sphere , 1997 .

[113]  Danesh K. Tafti,et al.  Comparison of some upwind-biased high-order formulations with a second-order central-difference scheme for time integration of the incompressible Navier-Stokes equations , 1996 .

[114]  W. Devenport,et al.  The structure and development of a wing-tip vortex , 1996, Journal of Fluid Mechanics.

[115]  Sherwin,et al.  Tetrahedral hp Finite Elements : Algorithms and Flow Simulations , 1996 .

[116]  George Em Karniadakis,et al.  A triangular spectral element method; applications to the incompressible Navier-Stokes equations , 1995 .

[117]  J. Boyd,et al.  A staggered spectral element model with application to the oceanic shallow , 1995 .

[118]  Ivo Babuska,et al.  The p and h-p Versions of the Finite Element Method, Basic Principles and Properties , 1994, SIAM Rev..

[119]  Paul Fischer,et al.  Spectral element methods for large scale parallel Navier—Stokes calculations , 1994 .

[120]  R. Eatock Taylor,et al.  Finite element analysis of two-dimensional non-linear transient water waves , 1994 .

[121]  Hong Ma,et al.  A spectral element basin model for the shallow water equations , 1993 .

[122]  Eitan Tadmor,et al.  Legendre pseudospectral viscosity method for nonlinear conservation laws , 1993 .

[123]  Géza Seriani,et al.  Numerical simulation of interface waves by high‐order spectral modeling techniques , 1992 .

[124]  S. Orszag,et al.  High-order splitting methods for the incompressible Navier-Stokes equations , 1991 .

[125]  Anthony T. Patera,et al.  A Legendre spectral element method for simulation of unsteady incompressible viscous free-surface flows , 1990 .

[126]  Ivo Babuška,et al.  The p - and h-p version of the finite element method, an overview , 1990 .

[127]  Chi-Wang Shu,et al.  The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case , 1990 .

[128]  E. Tadmor,et al.  Convergence of spectral methods for nonlinear conservation laws. Final report , 1989 .

[129]  A. Patera.  A spectral element method for fluid dynamics: Laminar flow in a channel expansion , 1984 .

[130]  M. G. Duffy,et al.  Quadrature Over a Pyramid or Cube of Integrands with a Singularity at a Vertex , 1982 .

[131]  D. Gottlieb,et al.  Numerical analysis of spectral methods : theory and applications , 1977 .

[132]  D. Gottlieb,et al.  Numerical analysis of spectral methods , 1977 .

[133]  D. Griffin,et al.  Finite-Element Analysis , 1975 .

[134]  W. H. Reed,et al.  Triangular mesh methods for the neutron transport equation , 1973 .

[135]  H. Kreiss,et al.  Comparison of accurate methods for the integration of hyperbolic equations , 1972 .

[136]  Vladimir E. Zakharov,et al.  Stability of periodic waves of finite amplitude on the surface of a deep fluid , 1968 .

[137]  D. Peregrine.  Long waves on a beach , 1967, Journal of Fluid Mechanics.