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, 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, 06/2016, 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 Scientific Computing, ISSN 0885-7474, 10/2012, Volume 53, Issue 1, pp. 222 - 247

High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in (Parés, SIAM J. Numer. Anal. 44:300–321, 2006;...

Computational Mathematics and Numerical Analysis | Nonconservative hyperbolic systems | Two-medium flows | Algorithms | Path-conservative schemes | Theoretical, Mathematical and Computational Physics | High order finite volume WENO scheme | Appl.Mathematics/Computational Methods of Engineering | Primitive Euler equations | Mathematics | Subcell resolution | Exact Riemann solver | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | HYPERBOLIC SYSTEMS | SIMULATION | ENO SCHEMES | RIEMANN PROBLEM | GHOST FLUID METHOD | DISCONTINUOUS GALERKIN METHODS | GAS | CONSERVATION-LAWS | MULTI-MEDIUM FLOW

Computational Mathematics and Numerical Analysis | Nonconservative hyperbolic systems | Two-medium flows | Algorithms | Path-conservative schemes | Theoretical, Mathematical and Computational Physics | High order finite volume WENO scheme | Appl.Mathematics/Computational Methods of Engineering | Primitive Euler equations | Mathematics | Subcell resolution | Exact Riemann solver | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | HYPERBOLIC SYSTEMS | SIMULATION | ENO SCHEMES | RIEMANN PROBLEM | GHOST FLUID METHOD | DISCONTINUOUS GALERKIN METHODS | GAS | CONSERVATION-LAWS | MULTI-MEDIUM FLOW

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 03/2019, Volume 89, Issue 8, pp. 304 - 325

Summary High‐order finite volume schemes for conservation laws are very useful in applications, due to their ability to compute accurate solutions on quite...

path‐conservative scheme | well‐balanced scheme | CWENO reconstruction | shallow water equations | finite volume scheme | well-balanced scheme | path-conservative scheme | PHYSICS, FLUIDS & PLASMAS | IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | FULL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYSTEMS | CENTRAL WENO SCHEME | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | Reconstruction | Shallow water equations | Conservation laws | Accuracy | Computer simulation | Solutions | Volume | Procedures | Shallow water | Equations | Mathematics - Numerical Analysis

path‐conservative scheme | well‐balanced scheme | CWENO reconstruction | shallow water equations | finite volume scheme | well-balanced scheme | path-conservative scheme | PHYSICS, FLUIDS & PLASMAS | IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | FULL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYSTEMS | CENTRAL WENO SCHEME | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | Reconstruction | Shallow water equations | Conservation laws | Accuracy | Computer simulation | Solutions | Volume | Procedures | Shallow water | Equations | Mathematics - Numerical Analysis

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 04/2013, Volume 257, pp. 47 - 64

In this article the weakly compressible two-phase diffuse interface method (DIM) for the simulation of complex two-dimensional non-hydrostatic free surface...

Unstructured meshes | Baer–Nunziato model | Diffuse interface method (DIM) | Compressible two-phase flows | High order path-conservative WENO finite volume schemes | Complex free surface flows | Baer-Nunziato model | HYPERBOLIC SYSTEMS | WENO SCHEMES | ESSENTIALLY NONOSCILLATORY SCHEMES | SHALLOW-WATER EQUATIONS | RIEMANN PROBLEM | SOURCE TERMS | GODUNOV METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | VOLUME SCHEMES | FINITE-ELEMENT-METHOD

Unstructured meshes | Baer–Nunziato model | Diffuse interface method (DIM) | Compressible two-phase flows | High order path-conservative WENO finite volume schemes | Complex free surface flows | Baer-Nunziato model | HYPERBOLIC SYSTEMS | WENO SCHEMES | ESSENTIALLY NONOSCILLATORY SCHEMES | SHALLOW-WATER EQUATIONS | RIEMANN PROBLEM | SOURCE TERMS | GODUNOV METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | VOLUME SCHEMES | FINITE-ELEMENT-METHOD

Journal Article

Computers and Fluids, ISSN 0045-7930, 09/2017, Volume 154, pp. 102 - 122

•New path-conservative SPH method for nonconservative hyperbolic PDE.•Well-balanced SPH schemes for shallow water systems.•SPH based on Riemann...

Osher (DOT) | and HLLEM | Single and two-layer shallow water equations and Pitman & Le model | Well-balanced SPH schemes | Comparison of different approximate Riemann solvers: Rusanov | Baer Nunziato model of compressible multiphase flow | Smoothed Particle Hydrodynamics (SPH) based on Riemann solvers | Path-conservative SPH schemes for non-conservative hyperbolic PDE | HLLEM | RIEMANN SOLVER | WENO SCHEMES | RECONSTRUCTION | EQUATIONS | MODEL | SIMULATION | Comparison of different approximate | SOURCE TERMS | GODUNOV METHOD | ORDER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Riemann solvers: Rusanov | FINITE-VOLUME SCHEMES | Fluid dynamics | Conservatism

Osher (DOT) | and HLLEM | Single and two-layer shallow water equations and Pitman & Le model | Well-balanced SPH schemes | Comparison of different approximate Riemann solvers: Rusanov | Baer Nunziato model of compressible multiphase flow | Smoothed Particle Hydrodynamics (SPH) based on Riemann solvers | Path-conservative SPH schemes for non-conservative hyperbolic PDE | HLLEM | RIEMANN SOLVER | WENO SCHEMES | RECONSTRUCTION | EQUATIONS | MODEL | SIMULATION | Comparison of different approximate | SOURCE TERMS | GODUNOV METHOD | ORDER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Riemann solvers: Rusanov | FINITE-VOLUME SCHEMES | Fluid dynamics | Conservatism

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 2011, Volume 200, Issue 9, pp. 1204 - 1219

In this article we propose a simple and efficient diffuse interface (interface- capturing) two-phase algorithm for the simulation of complex non-hydrostatic...

Interface capturing method | Reduced Baer-Nunziato model | Two-phase diffuse interface method (DIM) | Path-conservative WENO finite volume schemes on unstructured meshes | Dambreak and wave impact problems | Complex non-hydrostatic free surface flows with overtopping | HYPERBOLIC SYSTEMS | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | SMOOTHED PARTICLE HYDRODYNAMICS | SHALLOW-WATER EQUATIONS | GHOST FLUID METHOD | SOURCE TERMS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | ENGINEERING, MULTIDISCIPLINARY | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Models | Algorithms | Analysis | Methods

Interface capturing method | Reduced Baer-Nunziato model | Two-phase diffuse interface method (DIM) | Path-conservative WENO finite volume schemes on unstructured meshes | Dambreak and wave impact problems | Complex non-hydrostatic free surface flows with overtopping | HYPERBOLIC SYSTEMS | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | SMOOTHED PARTICLE HYDRODYNAMICS | SHALLOW-WATER EQUATIONS | GHOST FLUID METHOD | SOURCE TERMS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | ENGINEERING, MULTIDISCIPLINARY | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Models | Algorithms | Analysis | Methods

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

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