International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 05/2017, Volume 84, Issue 2, pp. 76 - 106

Summary In this paper, we present a new family of direct arbitrary–Lagrangian–Eulerian (ALE) finite volume schemes for the solution of hyperbolic balance laws...

MOOD | hyperbolic conservation laws | MHD | direct Arbitrary–Lagrangian–Eulerian | quadrature‐free | Euler equations | high order of accuracy in space and time | unstructured mesh | ADER | quadrature-free | DISCONTINUOUS GALERKIN DISCRETIZATION | HLLC RIEMANN SOLVER | TRIANGULAR MESHES | direct Arbitrary-Lagrangian-Eulerian | PHYSICS, FLUIDS & PLASMAS | GENERAL UNSTRUCTURED GRIDS | ESSENTIALLY NONOSCILLATORY SCHEMES | COMPRESSIBLE EULER EQUATIONS | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CENTERED LAGRANGIAN HYDRODYNAMICS | BALANCE LAWS | HYPERBOLIC CONSERVATION-LAWS | Fluid dynamics | Algorithms | Beer | Reconstruction | Accuracy | Computational fluid dynamics | Mathematical analysis | Mathematical models | Moods | Constraining

MOOD | hyperbolic conservation laws | MHD | direct Arbitrary–Lagrangian–Eulerian | quadrature‐free | Euler equations | high order of accuracy in space and time | unstructured mesh | ADER | quadrature-free | DISCONTINUOUS GALERKIN DISCRETIZATION | HLLC RIEMANN SOLVER | TRIANGULAR MESHES | direct Arbitrary-Lagrangian-Eulerian | PHYSICS, FLUIDS & PLASMAS | GENERAL UNSTRUCTURED GRIDS | ESSENTIALLY NONOSCILLATORY SCHEMES | COMPRESSIBLE EULER EQUATIONS | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CENTERED LAGRANGIAN HYDRODYNAMICS | BALANCE LAWS | HYPERBOLIC CONSERVATION-LAWS | Fluid dynamics | Algorithms | Beer | Reconstruction | Accuracy | Computational fluid dynamics | Mathematical analysis | Mathematical models | Moods | Constraining

Journal Article

Archives of Computational Methods in Engineering, ISSN 1134-3060, 11/2017, Volume 24, Issue 4, pp. 751 - 801

In this work we develop a new class of high order accurate Arbitrary-Lagrangian–Eulerian (ALE) one-step finite volume schemes for the solution of nonlinear...

Engineering | Mathematical and Computational Engineering | DISCONTINUOUS GALERKIN SCHEMES | GENERALIZED RIEMANN PROBLEM | COMPRESSIBLE 2-PHASE FLOW | ESSENTIALLY NONOSCILLATORY SCHEMES | GODUNOV-TYPE SCHEMES | FREE-SURFACE FLOWS | SHALLOW-WATER SYSTEMS | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | TO-DETONATION TRANSITION | ENGINEERING, MULTIDISCIPLINARY | SCALAR CONSERVATION-LAWS | Algorithms | Fluid dynamics | Analysis | Differential equations | Beer | Magnetohydrodynamics | Divergence | Preforms | Deformation | Compressibility | Partial differential equations | Fluid flow | Finite element method | Operators (mathematics) | Accuracy | Robustness (mathematics) | Mathematical analysis | Polynomials | Mathematical models | Nonlinear systems | Boundary element method | Computational fluid dynamics | Gas dynamics | Hydrodynamics | Hydrodynamic equations | Euler-Lagrange equation | Velocity | Numerical analysis | Reference systems

Engineering | Mathematical and Computational Engineering | DISCONTINUOUS GALERKIN SCHEMES | GENERALIZED RIEMANN PROBLEM | COMPRESSIBLE 2-PHASE FLOW | ESSENTIALLY NONOSCILLATORY SCHEMES | GODUNOV-TYPE SCHEMES | FREE-SURFACE FLOWS | SHALLOW-WATER SYSTEMS | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | TO-DETONATION TRANSITION | ENGINEERING, MULTIDISCIPLINARY | SCALAR CONSERVATION-LAWS | Algorithms | Fluid dynamics | Analysis | Differential equations | Beer | Magnetohydrodynamics | Divergence | Preforms | Deformation | Compressibility | Partial differential equations | Fluid flow | Finite element method | Operators (mathematics) | Accuracy | Robustness (mathematics) | Mathematical analysis | Polynomials | Mathematical models | Nonlinear systems | Boundary element method | Computational fluid dynamics | Gas dynamics | Hydrodynamics | Hydrodynamic equations | Euler-Lagrange equation | Velocity | Numerical analysis | Reference systems

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

Journal of Computational Physics, ISSN 0021-9991, 10/2017, Volume 346, pp. 449 - 479

We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the...

Hyperbolic and parabolic PDE | Arbitrary-Lagrangian–Eulerian (ALE) Discontinuous Galerkin (DG) schemes | Moving unstructured meshes with local rezoning | Inertial Confinement Fusion (ICF) flows | High order of accuracy in space and time | Euler, MHD and Navier–Stokes equations | TRIANGULAR MESHES | ELEMENT-METHOD | TETRAHEDRAL MESHES | HIGH-ORDER | PHYSICS, MATHEMATICAL | GODUNOV-TYPE SCHEMES | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | ADER SCHEMES | BALANCE LAWS | Arbitrary-Lagrangian-Eulerian (ALE) | Discontinuous Galerkin (DG) schemes | Euler, MHD and Navier-Stokes equations | HYPERBOLIC CONSERVATION-LAWS | Analysis | Laser-plasma interactions | Algorithms | Pellet fusion

Hyperbolic and parabolic PDE | Arbitrary-Lagrangian–Eulerian (ALE) Discontinuous Galerkin (DG) schemes | Moving unstructured meshes with local rezoning | Inertial Confinement Fusion (ICF) flows | High order of accuracy in space and time | Euler, MHD and Navier–Stokes equations | TRIANGULAR MESHES | ELEMENT-METHOD | TETRAHEDRAL MESHES | HIGH-ORDER | PHYSICS, MATHEMATICAL | GODUNOV-TYPE SCHEMES | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | ADER SCHEMES | BALANCE LAWS | Arbitrary-Lagrangian-Eulerian (ALE) | Discontinuous Galerkin (DG) schemes | Euler, MHD and Navier-Stokes equations | HYPERBOLIC CONSERVATION-LAWS | Analysis | Laser-plasma interactions | Algorithms | Pellet fusion

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 07/2019, Volume 78, Issue 2, pp. 362 - 380

The aim of this paper is to propose a new simple and robust numerical flux of the centered type in the context of Arbitrary-Lagrangian–Eulerian (ALE) finite...

Arbitrary-Lagrangian–Eulerian (ALE) | FORCE | High order of accuracy in space and time | Stiff source terms | Numerical flux | Conservative and non-conservative hyperbolic PDE | ADER | DISCONTINUOUS GALERKIN DISCRETIZATION | TRIANGULAR MESHES | MATHEMATICS, APPLIED | TETRAHEDRAL MESHES | RIEMANN SOLVER | HYDRODYNAMICS | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | Conservative and non-conservativen hyperbolic PDE | TO-DETONATION TRANSITION | ADER SCHEMES | Arbitrary-Lagrangian-Eulerian (ALE) | FINITE-VOLUME SCHEMES | Fluid dynamics | Analysis | Algorithms | Magnetohydrodynamics | Nonlinear equations | Compressibility | Computational fluid dynamics | Gas dynamics | Triangles | Flux | Euler-Lagrange equation | Finite element method | Operators (mathematics) | Robustness (mathematics) | Eigenvalues | Tetrahedrons | Nonlinear systems | Hyperbolic systems

Arbitrary-Lagrangian–Eulerian (ALE) | FORCE | High order of accuracy in space and time | Stiff source terms | Numerical flux | Conservative and non-conservative hyperbolic PDE | ADER | DISCONTINUOUS GALERKIN DISCRETIZATION | TRIANGULAR MESHES | MATHEMATICS, APPLIED | TETRAHEDRAL MESHES | RIEMANN SOLVER | HYDRODYNAMICS | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | Conservative and non-conservativen hyperbolic PDE | TO-DETONATION TRANSITION | ADER SCHEMES | Arbitrary-Lagrangian-Eulerian (ALE) | FINITE-VOLUME SCHEMES | Fluid dynamics | Analysis | Algorithms | Magnetohydrodynamics | Nonlinear equations | Compressibility | Computational fluid dynamics | Gas dynamics | Triangles | Flux | Euler-Lagrange equation | Finite element method | Operators (mathematics) | Robustness (mathematics) | Eigenvalues | Tetrahedrons | Nonlinear systems | Hyperbolic systems

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 06/2019, Volume 90, Issue 6, pp. 296 - 321

Summary In this paper, we present an efficient semi‐implicit scheme for the solution of the Reynolds‐averaged Navier‐Stokes equations for the simulation of...

nonhydrostatic | Voronoi mesh | high order | divergence‐free | semi‐implicit | free surface flows | hydrostatic | semi-implicit | divergence-free | NUMBER | COMPRESSIBLE FLOWS | ELEMENT-METHOD | PHYSICS, FLUIDS & PLASMAS | DISCONTINUOUS GALERKIN METHOD | MODEL | SEMIIMPLICIT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | FINITE-DIFFERENCE METHODS | VOLUME SCHEMES | ADVECTION | Viscosity | Reconstruction | Divergence | Fluid dynamics | Computer simulation | Trajectories | Velocity distribution | Velocity | Equations | Finite element method | Interpolation | Continuity equation | Free surfaces | Surface flow

nonhydrostatic | Voronoi mesh | high order | divergence‐free | semi‐implicit | free surface flows | hydrostatic | semi-implicit | divergence-free | NUMBER | COMPRESSIBLE FLOWS | ELEMENT-METHOD | PHYSICS, FLUIDS & PLASMAS | DISCONTINUOUS GALERKIN METHOD | MODEL | SEMIIMPLICIT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | FINITE-DIFFERENCE METHODS | VOLUME SCHEMES | ADVECTION | Viscosity | Reconstruction | Divergence | Fluid dynamics | Computer simulation | Trajectories | Velocity distribution | Velocity | Equations | Finite element method | Interpolation | Continuity equation | Free surfaces | Surface flow

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2019, Volume 387, pp. 481 - 521

•Theoretical comparison between hypoelastic and hyperelastic description of the dynamics of solids.•Wilkins model for hypoelasticity and...

Unified first order hyperbolic model of continuum mechanics | Symmetric hyperbolic thermodynamically compatible systems (SHTC) | Direct ALE | Path-conservative methods and stiff source terms | Arbitrary high-order ADER Discontinuous Galerkin and Finite Volume schemes | Viscoplasticity and elastoplasticity | DISCONTINUOUS GALERKIN SCHEMES | ELEMENT-METHOD | HIGH-ORDER | Arbitrary high-order ADER Discontinuous | PHYSICS, MATHEMATICAL | PLASTIC FLOW | RELATIVISTIC THERMODYNAMICS | NONCONSERVATIVE HYPERBOLIC SYSTEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ADER SCHEMES | CONSERVATION-LAWS | UNSTRUCTURED MESHES | Galerkin and Finite Volume schemes | FINITE-VOLUME SCHEMES | Comparative analysis | Thermodynamics | Formulations | Mathematical models | Galerkin method | Equations of state | Elastoplasticity | Elastic deformation | Physics | Astrophysics

Unified first order hyperbolic model of continuum mechanics | Symmetric hyperbolic thermodynamically compatible systems (SHTC) | Direct ALE | Path-conservative methods and stiff source terms | Arbitrary high-order ADER Discontinuous Galerkin and Finite Volume schemes | Viscoplasticity and elastoplasticity | DISCONTINUOUS GALERKIN SCHEMES | ELEMENT-METHOD | HIGH-ORDER | Arbitrary high-order ADER Discontinuous | PHYSICS, MATHEMATICAL | PLASTIC FLOW | RELATIVISTIC THERMODYNAMICS | NONCONSERVATIVE HYPERBOLIC SYSTEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ADER SCHEMES | CONSERVATION-LAWS | UNSTRUCTURED MESHES | Galerkin and Finite Volume schemes | FINITE-VOLUME SCHEMES | Comparative analysis | Thermodynamics | Formulations | Mathematical models | Galerkin method | Equations of state | Elastoplasticity | Elastic deformation | Physics | Astrophysics

Journal Article

Computers and Fluids, ISSN 0045-7930, 11/2013, Volume 86, pp. 405 - 432

•Arbitrary-Lagrangian–Eulerian (ALE) finite volume schemes for non-linear non-conservative hyperbolic systems.•High order accurate path-conservative Lagrangian...

Baer–Nunziato model | Arbitrary-Lagrangian–Eulerian (ALE) | WENO finite volume schemes on moving unstructured meshes | Path-conservative Lagrangian schemes | High order accuracy in space and time | Compressible multi-phase flows | Arbitrary-Lagrangian-Eulerian (ALE) | Baer-Nunziato model | RECTANGULAR TANK | ELEMENT-METHOD | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | FREE-SURFACE FLOWS | GHOST FLUID METHOD | SHALLOW-WATER SYSTEMS | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | TO-DETONATION TRANSITION | CONSERVATION-LAWS | Reconstruction | Accuracy | Fluids | Computational fluid dynamics | Mathematical analysis | Fluid flow | Polynomials | Galerkin methods

Baer–Nunziato model | Arbitrary-Lagrangian–Eulerian (ALE) | WENO finite volume schemes on moving unstructured meshes | Path-conservative Lagrangian schemes | High order accuracy in space and time | Compressible multi-phase flows | Arbitrary-Lagrangian-Eulerian (ALE) | Baer-Nunziato model | RECTANGULAR TANK | ELEMENT-METHOD | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | FREE-SURFACE FLOWS | GHOST FLUID METHOD | SHALLOW-WATER SYSTEMS | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | TO-DETONATION TRANSITION | CONSERVATION-LAWS | Reconstruction | Accuracy | Fluids | Computational fluid dynamics | Mathematical analysis | Fluid flow | Polynomials | 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