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This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov & Romenski, denoted as HPR model.
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Symmetric forms of thermodynamically compatible systems of conservation laws in continuum mechanics
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A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
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Sound generation in a mixing layer
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Statistical mechanics of monatomic liquids
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The local discontinuous Galerkin method for time-dependent convection diffusion systems
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Elements of mechanics of continuous media
S.K. Godunov and E.I. Romenski · 1998
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The spectral-element method: an efficient tool to simulate the seismic response of 2d and 3d geological structures
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Hyperbolic systems of thermodynamically compatible conservation laws in continuum mechanics
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A discontinuous hp finite element method for convection-diffusion problems
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Introduction to the spectral-element method for 3-d seismic wave propagation
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Dynamics of monatomic liquids
E D Chisolm and D C Wallace · 2001
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Runge-Kutta discontinuous Galerkin methods for convection-dominated problems
B. Cockburn and C. W. Shu · 2001
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Thermodynamics and hyperbolic systems of balance laws in continuum mechanics
E.I. Romenski · 2001
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Towards very high order Godunov schemes
E.F. Toro, R.C. Millington, and L.A.M Nejad · 2001
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Unified analysis of discontinuous galerkin methods for elliptic problems
D.N. Arnold, F. Brezzi, B. Cockburn, and L.D. Marini · 2002
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ADER: A high order approach for linear hyperbolic systems in 2d
T. Schwartzkopff, C.D. Munz, and E.F. Toro · 2002
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ADER finite volume schemes for nonlinear reaction-diffusion equations
E.F. Toro and A. Hidalgo · 2009
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An eulerian finite-volume scheme for large elastoplastic deformations in solids
P.T. Barton, D. Drikakis, and E.I. Romenski · 2010
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Arbitrary high order PNPM schemes on unstructured meshes for the compressible Navier–Stokes equations
M. Dumbser · 2010
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FORCE schemes on unstructured meshes II: Non–conservative hyperbolic systems
M. Dumbser, A. Hidalgo, M. Castro, C. Parés, and E.F. Toro · 2010
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Thermodynamically consistent nonlinear model of elastoplastic maxwell medium
S.K. Godunov and I.M. Peshkov · 2010
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A reconstructed discontinuous Galerkin method for the compressible Navier–Stokes equations on arbitrary grids
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ADER: Arbitrary high order Godunov approach
V.A. Titarev and E.F. Toro · 2002
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Solution of the generalized Riemann problem for advection-reaction equations
E.F. Toro and V. A. Titarev · 2002
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A local discontinuous Galerkin method for KdV-type equations
J. Yan and C.W. Shu · 2002
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Local discontinuous Galerkin methods for partial differential equations with higher order derivatives
J. Yan and C.W. Shu · 2002
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Elements of continuum mechanics and conservation laws
S.K. Godunov and E.I. Romenski · 2003
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Fluid Mechanics, Course of Theoretical Physics, Volume 6
L. D. Landau and E. M. Lifshitz · 2004
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H. Luo, L. Luo, R. Nourgaliev, V.A. Mousseau, and N. Dinh · 2010
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A first-order system approach for diffusion equation. II: Unification of advection and diffusion
H. Nishikawa · 2010
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Conservative models and numerical methods for compressible two-phase flow
E. Romenski, D. Drikakis, and E. Toro · 2010
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WENO schemes for mixed–element unstructured meshes
V.A. Titarev, P. Tsoutsanis, and D. Drikakis · 2010
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On universal Osher–type schemes for general nonlinear hyperbolic conservation laws
M. Dumbser and E. F. Toro · 2011
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A simple extension of the Osher Riemann solver to non-conservative hyperbolic systems
M. Dumbser and E. F. Toro · 2011
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Explicit one–step time discretizations for discontinuous Galerkin and finite volume schemes based on local predictors
G. Gassner, M. Dumbser, F. Hindenlang, and C.D. Munz · 2011
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ADER schemes for nonlinear systems of stiff advection-diffusion-reaction equations
A. Hidalgo and M. Dumbser · 2011
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WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions
P. Tsoutsanis, V.A. Titarev, and D. Drikakis · 2011
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Two liquid states of matter: A dynamic line on a phase diagram
VV Brazhkin, Yu D Fomin, AG Lyapin, VN Ryzhov, and K Trachenko · 2012
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A conservation law formulation of nonlinear elasticity in general relativity
C. Gundlach, I. Hawke, and S. J. Erickson · 2012
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Efficient implementation of ADER schemes for Euler and magnetohydrodynamical flows on structured meshes – Speed comparisons with Runge–Kutta methods
D.S. Balsara, C. Meyer, M. Dumbser, H. Du, and Z. Xu · 2013
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Eulerian adaptive finite-difference method for high-velocity impact and penetration problems
P.T. Barton, R. Deiterding, D. Meiron, and D. Pullin · 2013
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Thermodynamic behaviour of supercritical matter
D Bolmatov, VV Brazhkin, and K Trachenko · 2013
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Simulation of compressible viscous flow in time–dependent domains
J. Cesenek, M. Feistauer, J. Horacek, V. Kucera, and J. Prokopova · 2013
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High-order unstructured Lagrangian one–step WENO finite volume schemes for non–conservative hyperbolic systems: Applications to compressible multi–phase flows
M. Dumbser and W. Boscheri · 2013
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ADER-WENO Finite Volume Schemes with Space-Time Adaptive Mesh Refinement
M. Dumbser, O. Zanotti, A. Hidalgo, and D.S. Balsara · 2013
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A reconstructed discontinuous Galerkin method based on a Hierarchical WENO reconstruction for compressible flows on tetrahedral grids
H. Luo, Y. Xia, S. Spiegel, R. Nourgaliev, and Z. Jiang · 2013
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Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties
L.O. Müller, C. Parés, and E.F. Toro · 2013
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Well-balanced high-order solver for blood flow in networks of vessels with variable properties
L.O. Müller and E.F. Toro · 2013
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A Direct Arbitrary-Lagrangian-Eulerian ADER-WENO Finite Volume Scheme on Unstructured Tetrahedral Meshes for Conservative and Nonconservative Hyperbolic Systems in 3D
W. Boscheri and M. Dumbser · 2014
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High Order Space-Time Adaptive ADER-WENO Finite Volume Schemes for Non-Conservative Hyperbolic Systems
M. Dumbser, A. Hidalgo, and O. Zanotti · 2014
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A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
M. Dumbser, O. Zanotti, R. Loubère, and S. Diot · 2014
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A new family of high order unstructured MOOD and ADER finite volume schemes for multidimensional systems of hyperbolic conservation laws
R. Loubère, M. Dumbser, and S. Diot · 2014
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Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes
G.I. Montecinos, L.O. Müller, and E.F. Toro · 2014
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Reformulations for general advection-diffusion-reaction equations and locally implicit ADER schemes
G.I. Montecinos and E.F. Toro · 2014
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A hyperbolic model for viscous newtonian flows
I. Peshkov and E. Romenski · 2014
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Shock capturing for discontinuous galerkin methods using finite volume subcells
M. Sonntag and C.D. Munz · 2014
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A staggered semi-implicit discontinuous Galerkin method for the two dimensional incompressible Navier–Stokes equations
M. Tavelli and M. Dumbser · 2014
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Advection-diffusion-reaction equations: Hyperbolization and high-order ADER discretizations
E.F. Toro and G.I. Montecinos · 2014
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Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers
D.S. Balsara and M. Dumbser · 2015
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Revealing the mechanism of the viscous-to-elastic crossover in liquids
D Bolmatov, M Zhernenkov, D Zav’yalov, S Stoupin, Y Q Cai, and A Cunsolo · 2015
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Irreversible mechanics and thermodynamics of two-phase continua experiencing stress-induced solid–fluid transitions
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A staggered space–time discontinuous Galerkin method for the incompressible Navier–Stokes equations on two–dimensional triangular meshes
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Implicit, semi-analytical solution of the generalized Riemann problem for stiff hyperbolic balance laws
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A high order special relativistic hydrodynamic and magnetohydrodynamic code with space-time adaptive mesh refinement
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Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement
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Space-time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori subcell finite volume limiting
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Approximate Osher–Solomon schemes for hyperbolic systems
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A new, efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems
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A conservative, weakly nonlinear semi–implicit finite volume scheme for the compressible Navier–Stokes equations with general equation of state
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