A New Thermodynamically Compatible Finite Volume Scheme for Magnetohydrodynamics

Thermodynamically compatible discretization of a compressible two-fluid model with two entropy inequalities ⋮ A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume / finite element scheme for the incompressible MHD equations ⋮ On Thermodynamically Compatible Finite Volume Schemes for Overdetermined Hyperbolic Systems ⋮ Exact and numerical solutions of the Riemann problem for a conservative model of compressible two-phase flows

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A simple extension of the Osher Riemann solver to non-conservative hyperbolic systems
Conservative models and numerical methods for compressible two-phase flow
A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations
A high-order nonconservative approach for hyperbolic equations in fluid dynamics
Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers
A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations
A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
Divergence correction techniques for Maxwell solvers based on a hyperbolic model
Hyperbolic systems of thermodynamically compatible conservation laws in continuum mechanics.
Hyperbolic divergence cleaning for the MHD equations
Ideal GLM-MHD: about the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations
Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws
Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes
An entropy stable finite volume scheme for the two dimensional Navier-Stokes equations on triangular grids
A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes
On high order ADER discontinuous Galerkin schemes for first order hyperbolic reformulations of nonlinear dispersive systems
On thermodynamically compatible finite volume methods and path-conservative ADER discontinuous Galerkin schemes for turbulent shallow water flows
A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations
A semi-implicit hybrid finite volume/finite element scheme for all Mach number flows on staggered unstructured meshes
Multidimensional HLLE Riemann solver: application to Euler and magnetohydrodynamic flows
Line integral solution of differential problems
Entropy Stable Finite Volume Scheme for Ideal Compressible MHD on 2-D Cartesian Meshes
Thermodynamic formalization of the fluid dynamics equations for a charged dielectric in an electromagnetic field
Accurate numerical discretizations of non-conservative hyperbolic systems
Entropy Conservative and Entropy Stable Schemes for Nonconservative Hyperbolic Systems
Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws
Line Integral Methods for Conservative Problems
Symmetric positive linear differential equations
Riemann Solvers and Numerical Methods for Fluid Dynamics
The Numerical Viscosity of Entropy Stable Schemes for Systems of Conservation Laws. I
On Universal Osher-Type Schemes for General Nonlinear Hyperbolic Conservation Laws
A new continuum model for general relativistic viscous heat-conducting media
On Thermodynamically Compatible Finite Volume Schemes for Continuum Mechanics
Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations
High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems
Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
Systems of Conservation Equations with a Convex Extension