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 Computational Physics, ISSN 0021-9991, 10/2014, Volume 275, pp. 484 - 523

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

MHD equations | High order of accuracy in space and time | Stiff source terms | Local rezoning | Baer–Nunziato model | Arbitrary-Lagrangian–Eulerian (ALE) finite volume schemes | Euler equations | Conservation laws and non-conservative hyperbolic PDE | WENO reconstruction on moving unstructured tetrahedral meshes | Compressible multi-phase flows | Arbitrary-Lagrangian-Eulerian (ALE) finite volume schemes | Baer-Nunziato model | TRIANGULAR MESHES | GENERALIZED RIEMANN PROBLEM | ASYMPTOTIC-EXPANSION | HYDRODYNAMICS | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | FREE-SURFACE FLOWS | GODUNOV METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DIFFERENCE METHODS | 2 DIMENSIONS | Analysis | Algorithms | Finite element method | Magnetohydrodynamics | Partial differential equations | Computation | Mathematical analysis | Mathematical models | Three dimensional

MHD equations | High order of accuracy in space and time | Stiff source terms | Local rezoning | Baer–Nunziato model | Arbitrary-Lagrangian–Eulerian (ALE) finite volume schemes | Euler equations | Conservation laws and non-conservative hyperbolic PDE | WENO reconstruction on moving unstructured tetrahedral meshes | Compressible multi-phase flows | Arbitrary-Lagrangian-Eulerian (ALE) finite volume schemes | Baer-Nunziato model | TRIANGULAR MESHES | GENERALIZED RIEMANN PROBLEM | ASYMPTOTIC-EXPANSION | HYDRODYNAMICS | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | FREE-SURFACE FLOWS | GODUNOV METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DIFFERENCE METHODS | 2 DIMENSIONS | Analysis | Algorithms | Finite element method | Magnetohydrodynamics | Partial differential equations | Computation | Mathematical analysis | Mathematical models | Three dimensional

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 10/2014, Volume 280, pp. 57 - 83

In this article a new high order accurate cell-centered Arbitrary-Lagrangian–Eulerian (ALE) Godunov-type finite volume method with time-accurate local time...

Hyperbolic conservation laws | Euler equations of compressible gas dynamics | Arbitrary-Lagrangian–Eulerian (ALE) Godunov-type finite volume methods | Time-accurate local time stepping (LTS) | High order Lagrangian ADER–WENO schemes | Magnetohydrodynamics equations (MHD) | High order Lagrangian ADER-WENO schemes | Arbitrary-Lagrangian-Eulerian (ALE) Godunov-type finite volume methods | TETRAHEDRAL MESHES | ADAPTIVE MESH REFINEMENT | EQUATIONS | DISCONTINUOUS GALERKIN METHOD | HIGH-ORDER | GAS-DYNAMICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | COMPRESSIBLE FLOW | BALANCE LAWS | SYSTEMS | UNSTRUCTURED MESHES | Environmental law | Reconstruction | Formulations | Algorithms | Gas dynamics | Mathematical analysis | Conservation | Magnetohydrodynamic equations | Finite volume method | Mathematics - Numerical Analysis

Hyperbolic conservation laws | Euler equations of compressible gas dynamics | Arbitrary-Lagrangian–Eulerian (ALE) Godunov-type finite volume methods | Time-accurate local time stepping (LTS) | High order Lagrangian ADER–WENO schemes | Magnetohydrodynamics equations (MHD) | High order Lagrangian ADER-WENO schemes | Arbitrary-Lagrangian-Eulerian (ALE) Godunov-type finite volume methods | TETRAHEDRAL MESHES | ADAPTIVE MESH REFINEMENT | EQUATIONS | DISCONTINUOUS GALERKIN METHOD | HIGH-ORDER | GAS-DYNAMICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | COMPRESSIBLE FLOW | BALANCE LAWS | SYSTEMS | UNSTRUCTURED MESHES | Environmental law | Reconstruction | Formulations | Algorithms | Gas dynamics | Mathematical analysis | Conservation | Magnetohydrodynamic equations | Finite volume method | Mathematics - Numerical Analysis

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 1/2016, Volume 66, Issue 1, pp. 240 - 274

In this paper we present a new and efficient quadrature-free formulation for the family of cell-centered high order accurate direct...

WENO reconstruction on moving unstructured meshes | Computational Mathematics and Numerical Analysis | Arbitrary-Lagrangian–Eulerian (ALE) | Algorithms | High order of accuracy in space and time | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Local rezoning | Quadrature-free flux integration | Hydrodynamics | Mathematics | Finite volume schemes | DISCONTINUOUS GALERKIN DISCRETIZATION | HLLC RIEMANN SOLVER | MATHEMATICS, APPLIED | TETRAHEDRAL MESHES | SIMULATION | REMAP | FLOW | NONCONSERVATIVE HYPERBOLIC SYSTEMS | GAS-DYNAMICS | Arbitrary-Lagrangian-Eulerian (ALE) | CONSERVATION-LAWS | Accuracy | Computational fluid dynamics | Integrals | Mathematical analysis | Flux | Mathematical models | Galerkin methods

WENO reconstruction on moving unstructured meshes | Computational Mathematics and Numerical Analysis | Arbitrary-Lagrangian–Eulerian (ALE) | Algorithms | High order of accuracy in space and time | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Local rezoning | Quadrature-free flux integration | Hydrodynamics | Mathematics | Finite volume schemes | DISCONTINUOUS GALERKIN DISCRETIZATION | HLLC RIEMANN SOLVER | MATHEMATICS, APPLIED | TETRAHEDRAL MESHES | SIMULATION | REMAP | FLOW | NONCONSERVATIVE HYPERBOLIC SYSTEMS | GAS-DYNAMICS | Arbitrary-Lagrangian-Eulerian (ALE) | CONSERVATION-LAWS | Accuracy | Computational fluid dynamics | Integrals | Mathematical analysis | Flux | Mathematical models | Galerkin methods

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2014, Volume 267, pp. 112 - 138

In this paper we use the genuinely multidimensional HLL Riemann solvers recently developed by Balsara et al. in [13] to construct a new class of...

Hyperbolic conservation laws | Arbitrary-Lagrangian–Eulerian (ALE) | ADER schemes | Multidimensional HLL and HLLC Riemann solvers | Direct ALE | Large time steps | High order WENO finite volume schemes | MHD equations | Moving unstructured meshes | Local rezoning | Euler equations | Arbitrary-Lagrangian-Eulerian (ALE) | MAGNETOHYDRODYNAMIC SIMULATIONS | FLUX-CORRECTED TRANSPORT | ASYMPTOTIC-EXPANSION | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | PHYSICS, MATHEMATICAL | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Arbitrary-Lagrangian Eulerian (ALE) | NONLINEAR HYPERBOLIC SYSTEMS | GODUNOV-TYPE METHODS | CONSERVATION-LAWS | Algorithms | Beer | Operators | Accuracy | Mathematical analysis | Nonlinearity | Computational efficiency | Galerkin methods | Riemann solver | Mathematics - Numerical Analysis

Hyperbolic conservation laws | Arbitrary-Lagrangian–Eulerian (ALE) | ADER schemes | Multidimensional HLL and HLLC Riemann solvers | Direct ALE | Large time steps | High order WENO finite volume schemes | MHD equations | Moving unstructured meshes | Local rezoning | Euler equations | Arbitrary-Lagrangian-Eulerian (ALE) | MAGNETOHYDRODYNAMIC SIMULATIONS | FLUX-CORRECTED TRANSPORT | ASYMPTOTIC-EXPANSION | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | PHYSICS, MATHEMATICAL | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Arbitrary-Lagrangian Eulerian (ALE) | NONLINEAR HYPERBOLIC SYSTEMS | GODUNOV-TYPE METHODS | CONSERVATION-LAWS | Algorithms | Beer | Operators | Accuracy | Mathematical analysis | Nonlinearity | Computational efficiency | Galerkin methods | Riemann solver | Mathematics - Numerical Analysis

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

Computers and Fluids, ISSN 0045-7930, 09/2016, Volume 136, pp. 48 - 66

•Arbitrary-Lagrangian-Eulerian finite volume scheme on moving curved unstructured meshes.•High order WENO reconstruction on moving curvilinear unstructured...

ADER approach on isoparametric Curvilinear meshes | WENO reconstruction on moving Unstructured curved meshes | Euler equations | High order of accuracy in space and time | Tocal rezoning | Direct Arbitrary-Lagrangian-Eulerian (ALE) finite volume schemes | RIEMANN SOLVERS | Curvilinear meshes | DISCONTINUOUS GALERKIN DISCRETIZATION | TRIANGULAR MESHES | Unstructured curved meshes | ADER approach on isoparametric | TETRAHEDRAL MESHES | WENO reconstruction on moving | VELOCITY BOUNDARY-CONDITION | PRESSURE RELAXATION | GAS-DYNAMICS | MULTIMATERIAL ALE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CONTINUUM-MECHANICS | HYPERBOLIC CONSERVATION-LAWS | Environmental law | Algorithms | Beer

ADER approach on isoparametric Curvilinear meshes | WENO reconstruction on moving Unstructured curved meshes | Euler equations | High order of accuracy in space and time | Tocal rezoning | Direct Arbitrary-Lagrangian-Eulerian (ALE) finite volume schemes | RIEMANN SOLVERS | Curvilinear meshes | DISCONTINUOUS GALERKIN DISCRETIZATION | TRIANGULAR MESHES | Unstructured curved meshes | ADER approach on isoparametric | TETRAHEDRAL MESHES | WENO reconstruction on moving | VELOCITY BOUNDARY-CONDITION | PRESSURE RELAXATION | GAS-DYNAMICS | MULTIMATERIAL ALE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CONTINUUM-MECHANICS | HYPERBOLIC CONSERVATION-LAWS | Environmental law | Algorithms | Beer

Journal Article

Computers and Fluids, ISSN 0045-7930, 08/2016, Volume 134-135, pp. 111 - 129

•High order cell-centered ADER-WENO ALE schemes for nonlinear hyperelasticity (GPR model).•Thermodynamically compatible symmetric hyperbolic formulation of...

Hyperbolic conservation laws with stiff source terms and non-conservative products | Unified first order hyperbolic formulation of continuum mechanics | Symmetric-hyperbolic Godunov-Peshkov-Romenski model (GPR model) of nonlinear hyperelasticity | Viscous heat conducting fluids and nonlinear elasto-plastic solids | High order direct Arbitrary-Lagrangian-Eulerian finite volume schemes | High order ADER-WENO schemes on moving unstructured meshes | TRIANGULAR MESHES | High order direct | TETRAHEDRAL MESHES | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | Arbitrary-Lagrangian-Eulerian finite volume schemes | NONCONSERVATIVE HYPERBOLIC SYSTEMS | Godunov-Peshkov-Romenski model (GPR model) of nonlinear hyperelasticity | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CONTINUUM-MECHANICS | Symmetric-hyperbolic | BALANCE LAWS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | DIFFUSE INTERFACE MODEL | Thermodynamics | Mechanical engineering | Analysis | Environmental law | Finite element method | Reconstruction | Numerical analysis | Mathematical analysis | Nonlinearity | Mathematical models | Continuum mechanics | Navier-Stokes equations | Numerical Analysis | Analysis of PDEs | Mathematics

Hyperbolic conservation laws with stiff source terms and non-conservative products | Unified first order hyperbolic formulation of continuum mechanics | Symmetric-hyperbolic Godunov-Peshkov-Romenski model (GPR model) of nonlinear hyperelasticity | Viscous heat conducting fluids and nonlinear elasto-plastic solids | High order direct Arbitrary-Lagrangian-Eulerian finite volume schemes | High order ADER-WENO schemes on moving unstructured meshes | TRIANGULAR MESHES | High order direct | TETRAHEDRAL MESHES | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | Arbitrary-Lagrangian-Eulerian finite volume schemes | NONCONSERVATIVE HYPERBOLIC SYSTEMS | Godunov-Peshkov-Romenski model (GPR model) of nonlinear hyperelasticity | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CONTINUUM-MECHANICS | Symmetric-hyperbolic | BALANCE LAWS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | DIFFUSE INTERFACE MODEL | Thermodynamics | Mechanical engineering | Analysis | Environmental law | Finite element method | Reconstruction | Numerical analysis | Mathematical analysis | Nonlinearity | Mathematical models | Continuum mechanics | Navier-Stokes equations | Numerical Analysis | Analysis of PDEs | Mathematics

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 12/2014, Volume 278, pp. 47 - 75

The purpose of this work is to propose a novel a posteriori finite volume subcell limiter technique for the Discontinuous Galerkin finite element method for...

ADER-DG | High performance computing (HPC) | Hyperbolic conservation laws | ADER-WENO | Arbitrary high-order discontinuous Galerkin schemes | MOOD paradigm | A posteriori subcell finite volume limiter | HERMITE WENO SCHEMES | HLLC RIEMANN SOLVER | EFFICIENT IMPLEMENTATION | PHYSICS, MATHEMATICAL | HIGH-ORDER SCHEMES | ARTIFICIAL VISCOSITY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | VOLUME SCHEMES | ADER SCHEMES | COMPRESSIBLE FLOW | DYNAMIC GRID MOTION | UNSTRUCTURED MESHES | Finite element method | Laws, regulations and rules | Analysis | Environmental law | Methods | Conservation laws | Accuracy | Computer simulation | Mathematical analysis | Galerkin methods | Constraining | Three dimensional | Mathematics - Numerical Analysis | Numerical Analysis | Mathematics

ADER-DG | High performance computing (HPC) | Hyperbolic conservation laws | ADER-WENO | Arbitrary high-order discontinuous Galerkin schemes | MOOD paradigm | A posteriori subcell finite volume limiter | HERMITE WENO SCHEMES | HLLC RIEMANN SOLVER | EFFICIENT IMPLEMENTATION | PHYSICS, MATHEMATICAL | HIGH-ORDER SCHEMES | ARTIFICIAL VISCOSITY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | VOLUME SCHEMES | ADER SCHEMES | COMPRESSIBLE FLOW | DYNAMIC GRID MOTION | UNSTRUCTURED MESHES | Finite element method | Laws, regulations and rules | Analysis | Environmental law | Methods | Conservation laws | Accuracy | Computer simulation | Mathematical analysis | Galerkin methods | Constraining | Three dimensional | Mathematics - Numerical Analysis | Numerical Analysis | Mathematics

Journal Article