Journal of Computational Physics, ISSN 0021-9991, 09/2013, Volume 248, pp. 257 - 286

We present the first high order one-step ADER-WENO finite volume scheme with adaptive mesh refinement (AMR) in multiple space dimensions. High order spatial...

Hyperbolic conservation laws | Adaptive mesh refinement (AMR) | Time accurate local timestepping | MHD equations | ADER approach | Space–time adaptive grids | High order WENO reconstruction | Euler equations | Local space–time DG predictor | Space-time adaptive grids | Local space-time DG predictor | GENERALIZED RIEMANN PROBLEM | TANG VORTEX SYSTEM | EFFICIENT IMPLEMENTATION | FLUID-DYNAMICS | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | HIGH-ORDER | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | Analysis | Algorithms

Hyperbolic conservation laws | Adaptive mesh refinement (AMR) | Time accurate local timestepping | MHD equations | ADER approach | Space–time adaptive grids | High order WENO reconstruction | Euler equations | Local space–time DG predictor | Space-time adaptive grids | Local space-time DG predictor | GENERALIZED RIEMANN PROBLEM | TANG VORTEX SYSTEM | EFFICIENT IMPLEMENTATION | FLUID-DYNAMICS | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | HIGH-ORDER | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | Analysis | Algorithms

Journal Article

Computers and Fluids, ISSN 0045-7930, 09/2015, Volume 118, pp. 204 - 224

•Very high order accurate adaptive mesh refinement (AMR) with local time stepping.•A posteriori subcell limiter for arbitrary high order accurate DG...

High order space–time adaptive mesh refinement (AMR) | Hyperbolic conservation laws | MOOD paradigm | ADER-DG and ADER-WENO finite volume schemes | A posteriori sub-cell finite volume limiter | Arbitrary high-order discontinuous Galerkin schemes | High order space-time adaptive mesh refinement (AMR) | HERMITE WENO SCHEMES | GENERALIZED RIEMANN PROBLEM | TANG VORTEX SYSTEM | EFFICIENT IMPLEMENTATION | ASYMPTOTIC-EXPANSION | HIGH-ORDER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MESH REFINEMENT | COMPRESSIBLE FLOW | CONSERVATION-LAWS | UNSTRUCTURED MESHES | Fluid dynamics | Environmental law | Magnetohydrodynamics | Fluids | Computational fluid dynamics | Mathematical analysis | Fluid flow | Mathematical models | Polynomials | Galerkin methods

High order space–time adaptive mesh refinement (AMR) | Hyperbolic conservation laws | MOOD paradigm | ADER-DG and ADER-WENO finite volume schemes | A posteriori sub-cell finite volume limiter | Arbitrary high-order discontinuous Galerkin schemes | High order space-time adaptive mesh refinement (AMR) | HERMITE WENO SCHEMES | GENERALIZED RIEMANN PROBLEM | TANG VORTEX SYSTEM | EFFICIENT IMPLEMENTATION | ASYMPTOTIC-EXPANSION | HIGH-ORDER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MESH REFINEMENT | COMPRESSIBLE FLOW | CONSERVATION-LAWS | UNSTRUCTURED MESHES | Fluid dynamics | Environmental law | Magnetohydrodynamics | Fluids | Computational fluid dynamics | Mathematical analysis | Fluid flow | Mathematical models | Polynomials | Galerkin methods

Journal Article

Computer Physics Communications, ISSN 0010-4655, 11/2017, Volume 220, pp. 297 - 318

This paper presents an arbitrary high-order accurate ADER Discontinuous Galerkin (DG) method on space–time adaptive meshes (AMR) for the solution of two...

Compressible Navier–Stokes equations | Arbitrary high-order discontinuous Galerkin schemes (ADER-DG) | Time-accurate local time stepping (LTS) | Viscous and resistive MHD equations | Space–time Adaptive Mesh Refinement (AMR) | A posteriori sub-cell ADER-WENO finite-volume limiter (MOOD paradigm) | HERMITE WENO SCHEMES | Space-time Adaptive Mesh Refinement (AMR) | GENERALIZED RIEMANN PROBLEM | ELEMENT-METHOD | HYPERBOLIC SYSTEMS | DISCONTINUOUS GALERKIN METHOD | HIGH-ORDER | PHYSICS, MATHEMATICAL | SOUND GENERATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Compressible Navier-Stokes equations | Fluid dynamics | Differential equations | Electric properties

Compressible Navier–Stokes equations | Arbitrary high-order discontinuous Galerkin schemes (ADER-DG) | Time-accurate local time stepping (LTS) | Viscous and resistive MHD equations | Space–time Adaptive Mesh Refinement (AMR) | A posteriori sub-cell ADER-WENO finite-volume limiter (MOOD paradigm) | HERMITE WENO SCHEMES | Space-time Adaptive Mesh Refinement (AMR) | GENERALIZED RIEMANN PROBLEM | ELEMENT-METHOD | HYPERBOLIC SYSTEMS | DISCONTINUOUS GALERKIN METHOD | HIGH-ORDER | PHYSICS, MATHEMATICAL | SOUND GENERATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Compressible Navier-Stokes equations | Fluid dynamics | Differential equations | Electric properties

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

Journal of Scientific Computing, ISSN 0885-7474, 7/2011, Volume 48, Issue 1, pp. 173 - 189

In this article we extend the high order ADER finite volume schemes introduced for stiff hyperbolic balance laws by Dumbser, Enaux and Toro (J. Comput. Phys....

Asymptotic preserving property | Computational Mathematics and Numerical Analysis | Algorithms | Compressible Navier–Stokes equations with chemical reactions | Theoretical, Mathematical and Computational Physics | Stiff source terms | Advection–diffusion–reaction equations | Appl.Mathematics/Computational Methods of Engineering | ADER approach | Mathematics | High order finite volume schemes | Compressible Navier-Stokes equations with chemical reactions | Advection-diffusion-reaction equations | MATHEMATICS, APPLIED | HIGH-ORDER | FLOW | ACCURACY | PNPM SCHEMES | CHEMISTRY | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Nonlinear dynamics | Algebra | Numerical analysis | Asymptotic properties | Laws | Mathematical analysis | Mathematical models | Dynamical systems

Asymptotic preserving property | Computational Mathematics and Numerical Analysis | Algorithms | Compressible Navier–Stokes equations with chemical reactions | Theoretical, Mathematical and Computational Physics | Stiff source terms | Advection–diffusion–reaction equations | Appl.Mathematics/Computational Methods of Engineering | ADER approach | Mathematics | High order finite volume schemes | Compressible Navier-Stokes equations with chemical reactions | Advection-diffusion-reaction equations | MATHEMATICS, APPLIED | HIGH-ORDER | FLOW | ACCURACY | PNPM SCHEMES | CHEMISTRY | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Nonlinear dynamics | Algebra | Numerical analysis | Asymptotic properties | Laws | Mathematical analysis | Mathematical models | Dynamical systems

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2013, Volume 235, pp. 934 - 969

ADER (Arbitrary DERivative in space and time) methods for the time-evolution of hyperbolic conservation laws have recently generated a fair bit of interest....

Reconstruction | Time stepping | WENO | MHD | Runge Kutta | Euler | ADER | Higher order schemes | DISCONTINUOUS GALERKIN SCHEMES | DIVERGENCE-FREE CONDITION | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | CONSTRAINED TRANSPORT METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NONLINEAR HYPERBOLIC SYSTEMS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Fluid dynamics | Magnetic fields | Analysis | Environmental law | Methods

Reconstruction | Time stepping | WENO | MHD | Runge Kutta | Euler | ADER | Higher order schemes | DISCONTINUOUS GALERKIN SCHEMES | DIVERGENCE-FREE CONDITION | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | CONSTRAINED TRANSPORT METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NONLINEAR HYPERBOLIC SYSTEMS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Fluid dynamics | Magnetic fields | Analysis | Environmental law | Methods

Journal Article

7.
Full Text
ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

Monthly Notices of the Royal Astronomical Society, ISSN 0035-8711, 07/2018, Volume 477, Issue 4, pp. 4543 - 4564

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved...

Shock waves | Black hole physics -MHD- relativistic processes | Methods: numerical | ELEMENT-METHOD | RIEMANN SOLVER | ADAPTIVE MESH REFINEMENT | MHD | 1ST-ORDER HYPERBOLIC FORMULATION | COMPRESSIBLE NAVIER-STOKES | HIGH-ORDER | methods: numerical | relativistic processes | black hole physics | ASTRONOMY & ASTROPHYSICS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | WENO LIMITERS | FINITE-VOLUME SCHEMES | shock waves

Shock waves | Black hole physics -MHD- relativistic processes | Methods: numerical | ELEMENT-METHOD | RIEMANN SOLVER | ADAPTIVE MESH REFINEMENT | MHD | 1ST-ORDER HYPERBOLIC FORMULATION | COMPRESSIBLE NAVIER-STOKES | HIGH-ORDER | methods: numerical | relativistic processes | black hole physics | ASTRONOMY & ASTROPHYSICS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | WENO LIMITERS | FINITE-VOLUME SCHEMES | shock waves

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 07/2015, Volume 292, pp. 56 - 87

In this paper we present a new family of efficient high order accurate direct Arbitrary-Lagrangian–Eulerian (ALE) one-step ADER-MOOD finite volume schemes for...

High performance computing (HPC) | Hyperbolic conservation laws | ADER schemes | Moving unstructured triangular and tetrahedral meshes | High order of accuracy in space and time | MOOD paradigm | A posteriori limiter | Arbitrary-Lagrangian–Eulerian | Arbitrary-Lagrangian-Eulerian | CONVECTION-DIFFUSION PROBLEM | DISCONTINUOUS GALERKIN DISCRETIZATION | HLLC RIEMANN SOLVER | TRIANGULAR MESHES | TETRAHEDRAL MESHES | ORDER DETECTION MOOD | ESSENTIALLY NONOSCILLATORY SCHEMES | PHYSICS, MATHEMATICAL | ARTIFICIAL VISCOSITY | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | UNSTRUCTURED MESHES | Environmental law | Analysis | Conservation laws | Compressibility | Discretization | Gas dynamics | Mathematical analysis | Cascades | Mathematical models | Moods

High performance computing (HPC) | Hyperbolic conservation laws | ADER schemes | Moving unstructured triangular and tetrahedral meshes | High order of accuracy in space and time | MOOD paradigm | A posteriori limiter | Arbitrary-Lagrangian–Eulerian | Arbitrary-Lagrangian-Eulerian | CONVECTION-DIFFUSION PROBLEM | DISCONTINUOUS GALERKIN DISCRETIZATION | HLLC RIEMANN SOLVER | TRIANGULAR MESHES | TETRAHEDRAL MESHES | ORDER DETECTION MOOD | ESSENTIALLY NONOSCILLATORY SCHEMES | PHYSICS, MATHEMATICAL | ARTIFICIAL VISCOSITY | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | UNSTRUCTURED MESHES | Environmental law | Analysis | Conservation laws | Compressibility | Discretization | Gas dynamics | Mathematical analysis | Cascades | Mathematical models | Moods

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2014, Volume 275, pp. 415 - 442

Following Cattaneo's original idea, in this article we first present two relaxation formulations for time-dependent, non-linear systems of...

ADER high-order schemes | Relaxation methods | Generalised Riemann problems | Advection–diffusion–reaction equations | Cauchy–Kowalewski procedure | Cauchy-Kowalewski procedure | Advection-diffusion-reaction equations | HIGH-ORDER | SOLVERS | BLOOD-FLOW | PHYSICS, MATHEMATICAL | RIEMANN PROBLEM | 1ST-ORDER SYSTEM APPROACH | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PNPM SCHEMES | LEQUATION | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | Compressibility | Balancing | Mathematical analysis | Ingredients | Nonlinearity | Mathematical models | Dynamical systems | Navier-Stokes equations

ADER high-order schemes | Relaxation methods | Generalised Riemann problems | Advection–diffusion–reaction equations | Cauchy–Kowalewski procedure | Cauchy-Kowalewski procedure | Advection-diffusion-reaction equations | HIGH-ORDER | SOLVERS | BLOOD-FLOW | PHYSICS, MATHEMATICAL | RIEMANN PROBLEM | 1ST-ORDER SYSTEM APPROACH | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PNPM SCHEMES | LEQUATION | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | Compressibility | Balancing | Mathematical analysis | Ingredients | Nonlinearity | Mathematical models | Dynamical systems | Navier-Stokes equations

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, 2009, Volume 228, Issue 7, pp. 2480 - 2516

The present paper introduces a class of finite volume schemes of increasing order of accuracy in space and time for hyperbolic systems that are in conservation...

Magnetohydrodynamics | Numerical methods | ADER | WENO | Unsteady compressible flow | DISCONTINUOUS GALERKIN SCHEMES | VARIATION DIMINISHING SCHEME | ADAPTIVE MESH REFINEMENT | ESSENTIALLY NONOSCILLATORY SCHEMES | POLARIZED ALFVEN WAVES | HIGH-ORDER | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NONLINEAR HYPERBOLIC SYSTEMS | CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | Flexible response (Strategy) | Fluid dynamics | Magnetic fields | Deterrence (Strategy) | Analysis | Reconstruction | Accuracy | Mathematical analysis | Fluid flow | MHD | Mathematical models | Physics - Computational Physics

Magnetohydrodynamics | Numerical methods | ADER | WENO | Unsteady compressible flow | DISCONTINUOUS GALERKIN SCHEMES | VARIATION DIMINISHING SCHEME | ADAPTIVE MESH REFINEMENT | ESSENTIALLY NONOSCILLATORY SCHEMES | POLARIZED ALFVEN WAVES | HIGH-ORDER | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NONLINEAR HYPERBOLIC SYSTEMS | CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | Flexible response (Strategy) | Fluid dynamics | Magnetic fields | Deterrence (Strategy) | Analysis | Reconstruction | Accuracy | Mathematical analysis | Fluid flow | MHD | Mathematical models | Physics - Computational Physics

Journal Article