Journal of Computational Physics, ISSN 0021-9991, 08/2018, Volume 366, pp. 386 - 414

In this paper we propose a new high order accurate space–time discontinuous Galerkin (DG) finite element scheme for the solution of the linear elastic wave...

Energy stability | High order schemes | Staggered unstructured meshes | Large time steps | Linear elasticity | Space–time discontinuous Galerkin methods | HETEROGENEOUS MEDIA | 1ST-ORDER HYPERBOLIC FORMULATION | WAVE-PROPAGATION PROBLEMS | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATIONS | STEPPING METHODS | FREE-SURFACE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Space-time discontinuous Galerkin methods | NAVIER-STOKES EQUATIONS | STABILITY ANALYSIS | ADER SCHEMES | DYNAMIC GRID MOTION | Mathematics - Numerical Analysis

Energy stability | High order schemes | Staggered unstructured meshes | Large time steps | Linear elasticity | Space–time discontinuous Galerkin methods | HETEROGENEOUS MEDIA | 1ST-ORDER HYPERBOLIC FORMULATION | WAVE-PROPAGATION PROBLEMS | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATIONS | STEPPING METHODS | FREE-SURFACE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Space-time discontinuous Galerkin methods | NAVIER-STOKES EQUATIONS | STABILITY ANALYSIS | ADER SCHEMES | DYNAMIC GRID MOTION | Mathematics - Numerical Analysis

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 12/2014, Volume 76, Issue 10, pp. 737 - 778

SUMMARYIn this paper, we present a class of high‐order accurate cell‐centered arbitrary Lagrangian–Eulerian (ALE) one‐step ADER weighted essentially...

node solvers | Euler equations of compressible gas dynamics | multifluid flows | MHD equations | moving unstructured meshes | relativistic MHD equations (RMHD) | high‐order ADER‐WENO ALE finite volume schemes | cell‐centered direct ALE | Cell-centered direct ALE | Relativistic MHD equations (RMHD) | Moving unstructured meshes | high-order ADER-WENO ALE finite volume schemes | Multifluid flows | Node solvers | HLLC RIEMANN SOLVER | DISCONTINUOUS GALERKIN DISCRETIZATION | TETRAHEDRAL MESHES | PHYSICS, FLUIDS & PLASMAS | ESSENTIALLY NONOSCILLATORY SCHEMES | NONCONSERVATIVE HYPERBOLIC SYSTEMS | FREE-SURFACE FLOWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CENTERED LAGRANGIAN HYDRODYNAMICS | cell-centered direct ALE | NUMERICAL-SIMULATION | FINITE-VOLUME SCHEMES | EULER EQUATIONS | High-order ADER-WENO ALE finite volume schemes | Fluid dynamics | Beer | Magnetohydrodynamics | Computational fluid dynamics | Partial differential equations | Mathematical analysis | Conservation | Fluid flow | Solvers | Mathematical models

node solvers | Euler equations of compressible gas dynamics | multifluid flows | MHD equations | moving unstructured meshes | relativistic MHD equations (RMHD) | high‐order ADER‐WENO ALE finite volume schemes | cell‐centered direct ALE | Cell-centered direct ALE | Relativistic MHD equations (RMHD) | Moving unstructured meshes | high-order ADER-WENO ALE finite volume schemes | Multifluid flows | Node solvers | HLLC RIEMANN SOLVER | DISCONTINUOUS GALERKIN DISCRETIZATION | TETRAHEDRAL MESHES | PHYSICS, FLUIDS & PLASMAS | ESSENTIALLY NONOSCILLATORY SCHEMES | NONCONSERVATIVE HYPERBOLIC SYSTEMS | FREE-SURFACE FLOWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CENTERED LAGRANGIAN HYDRODYNAMICS | cell-centered direct ALE | NUMERICAL-SIMULATION | FINITE-VOLUME SCHEMES | EULER EQUATIONS | High-order ADER-WENO ALE finite volume schemes | Fluid dynamics | Beer | Magnetohydrodynamics | Computational fluid dynamics | Partial differential equations | Mathematical analysis | Conservation | Fluid flow | Solvers | Mathematical models

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 01/2014, Volume 268, pp. 359 - 387

•Better than second order accurate space–time adaptive mesh refinement (AMR).•Time accurate local time stepping (LTS).•High order ADER-WENO finite volume...

Baer–Nunziato model | Adaptive mesh refinement (AMR) | Time accurate local time stepping | Path-conservative WENO finite volume schemes | High order ADER approach | Compressible multi-phase flows | Baer-Nunziato model | COMPRESSIBLE 2-PHASE FLOW | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | GHOST FLUID METHOD | FREE-SURFACE FLOWS | SHALLOW-WATER SYSTEMS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | TO-DETONATION TRANSITION | ENGINEERING, MULTIDISCIPLINARY | MESH REFINEMENT | 3-DIMENSIONAL CONSERVATION-LAWS | UNSTRUCTURED MESHES | Adaptive systems | Discretization | Multiphase flow | Mathematical analysis | Strategy | Mathematical models | Galerkin methods | Hyperbolic systems

Baer–Nunziato model | Adaptive mesh refinement (AMR) | Time accurate local time stepping | Path-conservative WENO finite volume schemes | High order ADER approach | Compressible multi-phase flows | Baer-Nunziato model | COMPRESSIBLE 2-PHASE FLOW | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | GHOST FLUID METHOD | FREE-SURFACE FLOWS | SHALLOW-WATER SYSTEMS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | TO-DETONATION TRANSITION | ENGINEERING, MULTIDISCIPLINARY | MESH REFINEMENT | 3-DIMENSIONAL CONSERVATION-LAWS | UNSTRUCTURED MESHES | Adaptive systems | Discretization | Multiphase flow | Mathematical analysis | Strategy | Mathematical models | Galerkin methods | Hyperbolic systems

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 04/2020, Volume 407, p. 109167

We present a new family of very high order accurate direct Arbitrary-Lagrangian-Eulerian (ALE) Finite Volume (FV) and Discontinuous Galerkin (DG) schemes for...

Fully-discrete one-step ADER approach for hyperbolic PDE | Arbitrary-Lagrangian-Eulerian (ALE) Finite Volume (FV) and Discontinuous Galerkin (DG) schemes | A posteriori sub-cell finite volume limiter | Arbitrary high order in space and time | Moving Voronoi tessellations with topology change | Compressible Euler and MHD equations | ELEMENT-METHOD | WELL-BALANCED SCHEMES | DISCONTINUOUS GALERKIN METHOD | COMPRESSIBLE NAVIER-STOKES | PHYSICS, MATHEMATICAL | NONCONSERVATIVE HYPERBOLIC SYSTEMS | FREE-SURFACE FLOWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ADER SCHEMES | CENTRAL WENO SCHEME | FINITE-VOLUME SCHEMES | DIFFUSE INTERFACE MODEL

Fully-discrete one-step ADER approach for hyperbolic PDE | Arbitrary-Lagrangian-Eulerian (ALE) Finite Volume (FV) and Discontinuous Galerkin (DG) schemes | A posteriori sub-cell finite volume limiter | Arbitrary high order in space and time | Moving Voronoi tessellations with topology change | Compressible Euler and MHD equations | ELEMENT-METHOD | WELL-BALANCED SCHEMES | DISCONTINUOUS GALERKIN METHOD | COMPRESSIBLE NAVIER-STOKES | PHYSICS, MATHEMATICAL | NONCONSERVATIVE HYPERBOLIC SYSTEMS | FREE-SURFACE FLOWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ADER SCHEMES | CENTRAL WENO SCHEME | FINITE-VOLUME SCHEMES | DIFFUSE INTERFACE MODEL

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2016, Volume 314, pp. 824 - 862

•High order schemes for a unified first order hyperbolic formulation of continuum mechanics.•The mathematical model applies simultaneously to fluid mechanics...

Unified first order hyperbolic formulation of nonlinear continuum mechanics | Path-conservative methods and stiff source terms | Fluid mechanics and solid mechanics | Viscous compressible fluids and elastic solids | Arbitrary high-order discontinuous Galerkin schemes | ADER–WENO finite volume schemes | ADER-WENO finite volume schemes | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | DIFFUSION-REACTION EQUATIONS | BLOOD-FLOW | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | SPECTRAL ELEMENT METHOD | GODUNOV-TYPE METHODS | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Mechanical engineering | Analysis | Differential equations | Computational fluid dynamics | Partial differential equations | Computation | Mathematical analysis | Fluid flow | Mathematical models | Continuum mechanics | Navier-Stokes equations | Mathematics - Numerical Analysis | FLUIDS | STRAINS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | THERMAL CONDUCTION | MATHEMATICAL MODELS | WAVE PROPAGATION | RELAXATION | ASYMPTOTIC SOLUTIONS | FINITE ELEMENT METHOD | ELASTICITY | FLUID MECHANICS | THERMODYNAMICS | FLOW VISUALIZATION | HEAT FLUX

Unified first order hyperbolic formulation of nonlinear continuum mechanics | Path-conservative methods and stiff source terms | Fluid mechanics and solid mechanics | Viscous compressible fluids and elastic solids | Arbitrary high-order discontinuous Galerkin schemes | ADER–WENO finite volume schemes | ADER-WENO finite volume schemes | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | DIFFUSION-REACTION EQUATIONS | BLOOD-FLOW | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | SPECTRAL ELEMENT METHOD | GODUNOV-TYPE METHODS | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Mechanical engineering | Analysis | Differential equations | Computational fluid dynamics | Partial differential equations | Computation | Mathematical analysis | Fluid flow | Mathematical models | Continuum mechanics | Navier-Stokes equations | Mathematics - Numerical Analysis | FLUIDS | STRAINS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | THERMAL CONDUCTION | MATHEMATICAL MODELS | WAVE PROPAGATION | RELAXATION | ASYMPTOTIC SOLUTIONS | FINITE ELEMENT METHOD | ELASTICITY | FLUID MECHANICS | THERMODYNAMICS | FLOW VISUALIZATION | HEAT FLUX

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2017, Volume 348, pp. 298 - 342

In this paper, we propose a new unified first order hyperbolic model of Newtonian continuum mechanics coupled with electro-dynamics. The model is able to...

Unified first order hyperbolic model of continuum physics (fluid mechanics, solid mechanics, electro-dynamics) | Arbitrary high-order ADER Discontinuous Galerkin schemes | Symmetric hyperbolic thermodynamically compatible systems (SHTC) | Nonlinear hyperelasticity | Path-conservative methods and stiff source terms | Finite signal speeds of all physical processes | Galerkin schemes | GENERALIZED RIEMANN PROBLEM | TANG VORTEX SYSTEM | ADAPTIVE MESH REFINEMENT | DISCONTINUOUS GALERKIN METHOD | DIFFUSION-REACTION EQUATIONS | Arbitrary high-order ADER Discontinuous | PHYSICS, MATHEMATICAL | HIGH-VELOCITY IMPACT | KELVIN-HELMHOLTZ INSTABILITY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STIFF RELAXATION TERMS | CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | Thermodynamics | Fluid dynamics | Magnetic fields | Electric fields | Analysis | Differential equations | Physics - Fluid Dynamics

Unified first order hyperbolic model of continuum physics (fluid mechanics, solid mechanics, electro-dynamics) | Arbitrary high-order ADER Discontinuous Galerkin schemes | Symmetric hyperbolic thermodynamically compatible systems (SHTC) | Nonlinear hyperelasticity | Path-conservative methods and stiff source terms | Finite signal speeds of all physical processes | Galerkin schemes | GENERALIZED RIEMANN PROBLEM | TANG VORTEX SYSTEM | ADAPTIVE MESH REFINEMENT | DISCONTINUOUS GALERKIN METHOD | DIFFUSION-REACTION EQUATIONS | Arbitrary high-order ADER Discontinuous | PHYSICS, MATHEMATICAL | HIGH-VELOCITY IMPACT | KELVIN-HELMHOLTZ INSTABILITY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STIFF RELAXATION TERMS | CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | Thermodynamics | Fluid dynamics | Magnetic fields | Electric fields | Analysis | Differential equations | Physics - Fluid Dynamics

Journal Article

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, ISSN 0035-8711, 07/2019, Volume 487, Issue 1, pp. 1283 - 1314

There is a great need in several areas of astrophysics and space physics to carry out high order of accuracy, divergence-free MHD simulations on spherical...

DISCONTINUOUS GALERKIN SCHEMES | plasmas | ESSENTIALLY NONOSCILLATORY SCHEMES | methods: numerical | SOLVER | MULTIDIMENSIONAL RIEMANN PROBLEM | NUMERICAL-SOLUTION | MAGNETOHYDRODYNAMIC FLOWS | ADER SCHEMES | ASTRONOMY & ASTROPHYSICS | (magnetohydrodynamics) MHD | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME SCHEMES

DISCONTINUOUS GALERKIN SCHEMES | plasmas | ESSENTIALLY NONOSCILLATORY SCHEMES | methods: numerical | SOLVER | MULTIDIMENSIONAL RIEMANN PROBLEM | NUMERICAL-SOLUTION | MAGNETOHYDRODYNAMIC FLOWS | ADER SCHEMES | ASTRONOMY & ASTROPHYSICS | (magnetohydrodynamics) MHD | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME SCHEMES

Journal Article

Computer Physics Communications, ISSN 0010-4655, 03/2015, Volume 188, pp. 110 - 127

We present a high order one-step ADER–WENO finite volume scheme with space–time adaptive mesh refinement (AMR) for the solution of the special relativistic...

Magnetohydrodynamics | High order ADER–WENO finite volume scheme | Time-accurate local time stepping (LTS) | Space–time adaptive mesh refinement (AMR) | Special relativity | Space-time adaptive mesh refinement (AMR) | ADER-WENO finite volume scheme | High order | INSTABILITY | MHD | EQUATIONS | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | RADIATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | High order ADER-WENO finite volume scheme | EXPANSION | FLOWS | EXACT RIEMANN SOLVER | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Mechanical engineering | Algorithms | Wave propagation | Computational fluid dynamics | Mathematical analysis | Fluid flow | Magnetohydrodynamic equations | Hydrodynamics | Mathematical models | Runge-Kutta method | Galerkin methods

Magnetohydrodynamics | High order ADER–WENO finite volume scheme | Time-accurate local time stepping (LTS) | Space–time adaptive mesh refinement (AMR) | Special relativity | Space-time adaptive mesh refinement (AMR) | ADER-WENO finite volume scheme | High order | INSTABILITY | MHD | EQUATIONS | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | RADIATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | High order ADER-WENO finite volume scheme | EXPANSION | FLOWS | EXACT RIEMANN SOLVER | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Mechanical engineering | Algorithms | Wave propagation | Computational fluid dynamics | Mathematical analysis | Fluid flow | Magnetohydrodynamic equations | Hydrodynamics | Mathematical models | Runge-Kutta method | Galerkin methods

Journal Article

Geophysical Journal International, ISSN 0956-540X, 11/2007, Volume 171, Issue 2, pp. 665 - 694

Summary We present a new numerical method to solve the heterogeneous anelastic seismic wave equations with arbitrary high order of accuracy in space and time...

tetrahedral meshes | ADER approach | finite volume schemes | attenuation | high‐order accuracy | viscoelasticity | Viscoelasticity | Attenuation | High-order accuracy | Finite volume schemes | Tetrahedral meshes | HETEROGENEOUS MEDIA | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | ELASTIC-WAVES | GEOCHEMISTRY & GEOPHYSICS | GREEN-FUNCTIONS | SPECTRAL ELEMENT METHOD | PERFECTLY MATCHED LAYER | ADER SCHEMES | high-order accuracy | CONSERVATION-LAWS | NUMERICAL-SIMULATION

tetrahedral meshes | ADER approach | finite volume schemes | attenuation | high‐order accuracy | viscoelasticity | Viscoelasticity | Attenuation | High-order accuracy | Finite volume schemes | Tetrahedral meshes | HETEROGENEOUS MEDIA | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | ELASTIC-WAVES | GEOCHEMISTRY & GEOPHYSICS | GREEN-FUNCTIONS | SPECTRAL ELEMENT METHOD | PERFECTLY MATCHED LAYER | ADER SCHEMES | high-order accuracy | CONSERVATION-LAWS | NUMERICAL-SIMULATION

Journal Article