Journal of computational physics, ISSN 0021-9991, 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

Journal of computational physics, ISSN 0021-9991, 2016, Volume 319, pp. 163 - 199

In this paper we propose a simple, robust and accurate nonlinear a posteriori stabilization of the Discontinuous Galerkin (DG) finite element method for the...

Unstructured triangular and tetrahedral meshes | Element-wise checkpointing and restarting | MOOD paradigm | A posteriori sub-cell finite volume limiter | Conservation laws and hyperbolic PDE with non-conservative products | Arbitrary high-order discontinuous Galerkin schemes | HERMITE WENO SCHEMES | HLLC RIEMANN SOLVER | TANG VORTEX SYSTEM | ESSENTIALLY NONOSCILLATORY SCHEMES | PHYSICS, MATHEMATICAL | NONCONSERVATIVE HYPERBOLIC SYSTEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | TO-DETONATION TRANSITION | UNSPLIT GODUNOV METHOD | TROUBLED-CELL INDICATORS | SPACE-TIME EXPANSION | DYNAMIC GRID MOTION | Environmental law | Analysis | Methods | Discontinuity | Approximation | Computation | Mathematical analysis | Nonlinearity | Mathematical models | Galerkin methods | Standards | Numerical Analysis | Mathematics

Unstructured triangular and tetrahedral meshes | Element-wise checkpointing and restarting | MOOD paradigm | A posteriori sub-cell finite volume limiter | Conservation laws and hyperbolic PDE with non-conservative products | Arbitrary high-order discontinuous Galerkin schemes | HERMITE WENO SCHEMES | HLLC RIEMANN SOLVER | TANG VORTEX SYSTEM | ESSENTIALLY NONOSCILLATORY SCHEMES | PHYSICS, MATHEMATICAL | NONCONSERVATIVE HYPERBOLIC SYSTEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | TO-DETONATION TRANSITION | UNSPLIT GODUNOV METHOD | TROUBLED-CELL INDICATORS | SPACE-TIME EXPANSION | DYNAMIC GRID MOTION | Environmental law | Analysis | Methods | Discontinuity | Approximation | Computation | Mathematical analysis | Nonlinearity | Mathematical models | Galerkin methods | Standards | Numerical Analysis | Mathematics

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 12/2013, Volume 255, pp. 680 - 698

In this paper we present a new ultra efficient numerical method for solving kinetic equations. In this preliminary work, we present the scheme in the case of...

Semi-Lagrangian schemes | Boltzmann–BGK equation | Kinetic equations | Discrete velocity models | 3D simulation | Boltzmann-BGK equation | MONTE-CARLO | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTEGRATION | DISCRETE-VELOCITY MODEL | BOLTZMANN-EQUATION | CONVERGENCE | PHYSICS, MATHEMATICAL | Operators | Mathematical analysis | Mathematical models | Computational efficiency | Transport | Collision dynamics | Three dimensional

Semi-Lagrangian schemes | Boltzmann–BGK equation | Kinetic equations | Discrete velocity models | 3D simulation | Boltzmann-BGK equation | MONTE-CARLO | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTEGRATION | DISCRETE-VELOCITY MODEL | BOLTZMANN-EQUATION | CONVERGENCE | PHYSICS, MATHEMATICAL | Operators | Mathematical analysis | Mathematical models | Computational efficiency | Transport | Collision dynamics | Three dimensional

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2018, Volume 353, pp. 46 - 81

In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) (Dimarco and Loubère, 2013 [26]) originally constructed for solving the BGK equation,...

CUDA | 3D/3D | Boltzmann equation | Kinetic equations | OpenMP | MPI | Semi-Lagrangian schemes | Spectral schemes | GPU | RUNGE-KUTTA METHODS | KINETIC-EQUATIONS | DIFFERENCE SCHEME | PRESERVING AP SCHEMES | COLLISION OPERATOR | PHYSICS, MATHEMATICAL | FAST SPECTRAL METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FAST FOURIER-TRANSFORM | VLASOV EQUATION | RAREFIED-GAS DYNAMICS | DISCRETE VELOCITY MODELS | Computer science | Algorithms | Analysis | Methods | Mechanics | Mechanics of the fluids | Mathematics | Analysis of PDEs | Physics

CUDA | 3D/3D | Boltzmann equation | Kinetic equations | OpenMP | MPI | Semi-Lagrangian schemes | Spectral schemes | GPU | RUNGE-KUTTA METHODS | KINETIC-EQUATIONS | DIFFERENCE SCHEME | PRESERVING AP SCHEMES | COLLISION OPERATOR | PHYSICS, MATHEMATICAL | FAST SPECTRAL METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FAST FOURIER-TRANSFORM | VLASOV EQUATION | RAREFIED-GAS DYNAMICS | DISCRETE VELOCITY MODELS | Computer science | Algorithms | Analysis | Methods | Mechanics | Mechanics of the fluids | Mathematics | Analysis of PDEs | Physics

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 12/2013, Volume 255, pp. 699 - 719

In a recent paper we presented a new ultra efficient numerical method for solving kinetic equations of the Boltzmann type (Dimarco and Loubere, 2013) [17]. The...

Semi-Lagrangian schemes | Boltzmann–BGK equation | Kinetic equations | Discrete velocity models | High order scheme | Euler solver | Boltzmann-BGK equation | APPROXIMATION | ALGORITHM | MONTE-CARLO METHOD | SOLVER | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTEGRATION | BOLTZMANN-EQUATION | Accuracy | Fluids | Computational fluid dynamics | Computer simulation | Computation | Fluid flow | Mathematical models

Semi-Lagrangian schemes | Boltzmann–BGK equation | Kinetic equations | Discrete velocity models | High order scheme | Euler solver | Boltzmann-BGK equation | APPROXIMATION | ALGORITHM | MONTE-CARLO METHOD | SOLVER | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTEGRATION | BOLTZMANN-EQUATION | Accuracy | Fluids | Computational fluid dynamics | Computer simulation | Computation | Fluid flow | Mathematical models

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2018, Volume 354, pp. 86 - 110

In this paper we propose a third order accurate finite volume scheme based on a posteriori limiting of polynomial reconstructions within an...

Hyperbolic conservation laws | High order of accuracy in space and time | Adaptive Mesh Refinement | MOOD paradigm | Hydrodynamics | A posteriori limiter | [formula omitted] Adaptation | Entropy production | h/p Adaptation | COMPRESSIBLE FLOWS | EQUATIONS | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MOOD | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Sensors | Fluid dynamics | Laws, regulations and rules | Environmental law | Modeling and Simulation | Mathematics | Computer Science

Hyperbolic conservation laws | High order of accuracy in space and time | Adaptive Mesh Refinement | MOOD paradigm | Hydrodynamics | A posteriori limiter | [formula omitted] Adaptation | Entropy production | h/p Adaptation | COMPRESSIBLE FLOWS | EQUATIONS | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MOOD | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Sensors | Fluid dynamics | Laws, regulations and rules | Environmental law | Modeling and Simulation | Mathematics | Computer Science

Journal Article

Journal of computational physics, ISSN 0021-9991, 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

Journal of computational physics, ISSN 0021-9991, 2010, Volume 229, Issue 12, pp. 4724 - 4761

We present a new reconnection-based arbitrary-Lagrangian–Eulerian (ALE) method. The main elements in a standard ALE simulation are an explicit Lagrangian phase...

Voronoi mesh | Lagrangian hydrodynamics | Staggered scheme | Cell-centered scheme | Compressible flow | Arbitrary-Lagrangian–Eulerian | Mesh reconnection | Multi-dimensional unstructured polygonal mesh | Arbitrary-Lagrangian-Eulerian | COMPUTING METHOD | ALE HYDRODYNAMICS | ALGORITHM | MESH | SHOCK HYDRODYNAMICS | PHYSICS, MATHEMATICAL | COMPATIBLE FORMULATION | ARTIFICIAL VISCOSITY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION | DISCRETE | EFFICIENT | Fluid dynamics | Analysis | Methods | Beer

Voronoi mesh | Lagrangian hydrodynamics | Staggered scheme | Cell-centered scheme | Compressible flow | Arbitrary-Lagrangian–Eulerian | Mesh reconnection | Multi-dimensional unstructured polygonal mesh | Arbitrary-Lagrangian-Eulerian | COMPUTING METHOD | ALE HYDRODYNAMICS | ALGORITHM | MESH | SHOCK HYDRODYNAMICS | PHYSICS, MATHEMATICAL | COMPATIBLE FORMULATION | ARTIFICIAL VISCOSITY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION | DISCRETE | EFFICIENT | Fluid dynamics | Analysis | Methods | Beer

Journal Article

Journal of computational physics, ISSN 0021-9991, 2018, Volume 372, pp. 178 - 201

In this work, we consider the development of implicit-explicit total variation diminishing (TVD) methods (also termed SSP: strong stability preserving) for the...

Low Mach | SSP-TVD | IMEX schemes | High-order | Asymptotic preserving | Hyperbolic | NUMBER LIMIT | RUNGE-KUTTA METHODS | HYPERBOLIC SYSTEMS | ASYMPTOTIC PRESERVING SCHEME | INCOMPRESSIBLE LIMIT | GAS-DYNAMICS EQUATIONS | PHYSICS, MATHEMATICAL | CONVERGENCE ACCELERATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | ISENTROPIC EULER | UNSTRUCTURED MESHES | Mathematics - Numerical Analysis | Numerical Analysis | Analysis of PDEs | Mathematics

Low Mach | SSP-TVD | IMEX schemes | High-order | Asymptotic preserving | Hyperbolic | NUMBER LIMIT | RUNGE-KUTTA METHODS | HYPERBOLIC SYSTEMS | ASYMPTOTIC PRESERVING SCHEME | INCOMPRESSIBLE LIMIT | GAS-DYNAMICS EQUATIONS | PHYSICS, MATHEMATICAL | CONVERGENCE ACCELERATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | ISENTROPIC EULER | UNSTRUCTURED MESHES | Mathematics - Numerical Analysis | Numerical Analysis | Analysis of PDEs | Mathematics

Journal Article

Journal of scientific computing, ISSN 1573-7691, 2018, Volume 78, Issue 1, pp. 393 - 432

We introduce an extension of the fast semi-Lagrangian scheme developed in J Comput Phys 255:680–698 (2013) in an effort to increase the spatial accuracy of the...

Computational Mathematics and Numerical Analysis | Boltzmann equation | 65M25 | Theoretical, Mathematical and Computational Physics | Semi-Lagrangian schemes | 82C40 | Mathematics | Algorithms | Kinetic equations | High-order schemes | 76P05 | Mathematical and Computational Engineering | Rarefied gas dynamics | NUMERICAL-METHODS | MONTE-CARLO | MATHEMATICS, APPLIED | RUNGE-KUTTA METHODS | DISCRETE-VELOCITY MODEL | ALGORITHM | BOLTZMANN-EQUATION | Numerical Analysis

Computational Mathematics and Numerical Analysis | Boltzmann equation | 65M25 | Theoretical, Mathematical and Computational Physics | Semi-Lagrangian schemes | 82C40 | Mathematics | Algorithms | Kinetic equations | High-order schemes | 76P05 | Mathematical and Computational Engineering | Rarefied gas dynamics | NUMERICAL-METHODS | MONTE-CARLO | MATHEMATICS, APPLIED | RUNGE-KUTTA METHODS | DISCRETE-VELOCITY MODEL | ALGORITHM | BOLTZMANN-EQUATION | Numerical Analysis

Journal Article

International journal for numerical methods in engineering, ISSN 1097-0207, 2018, Volume 117, Issue 2, pp. 188 - 220

Summary Obtaining very high‐order accurate solutions in curved domains is a challenging task as the accuracy of discretization methods may dramatically reduce...

convection‐diffusion equation | general boundary conditions | least‐squares method | reconstruction for off‐site data method | very high‐order accurate finite volume scheme | arbitrary smooth curved boundaries | convection-diffusion equation | least-squares method | reconstruction for off-site data method | very high-order accurate finite volume scheme | LIMITER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | ESSENTIALLY NONOSCILLATORY SCHEMES | UNSTRUCTURED MESHES | Finite volume method | Boundary conditions | Boundaries | Meshing | Convection | Convergence | Finite element method | Domains | Accuracy | Algorithms | Transformations (mathematics) | Robustness (mathematics) | Discretization | Dirichlet problem | Polynomials | Mathematics

convection‐diffusion equation | general boundary conditions | least‐squares method | reconstruction for off‐site data method | very high‐order accurate finite volume scheme | arbitrary smooth curved boundaries | convection-diffusion equation | least-squares method | reconstruction for off-site data method | very high-order accurate finite volume scheme | LIMITER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | ESSENTIALLY NONOSCILLATORY SCHEMES | UNSTRUCTURED MESHES | Finite volume method | Boundary conditions | Boundaries | Meshing | Convection | Convergence | Finite element method | Domains | Accuracy | Algorithms | Transformations (mathematics) | Robustness (mathematics) | Discretization | Dirichlet problem | Polynomials | Mathematics

Journal Article