We introduce a simple and general framework for the construction of thermodynamically
compatible schemes for the numerical solution of overdetermined hyperbolic PDE systems …

In this paper we propose a novel thermodynamically compatible finite volume scheme for
the numerical solution of the equations of magnetohydrodynamics (MHD) in one and two …

In this chapter we describe a general methodology for developing high-order well-balanced
schemes for hyperbolic system with nonconservative products and/or source terms. We …

In this work a non-conservative balance law formulation is considered that encompasses the
rotating, compressible Euler equations for dry atmospheric flows. We develop a semi …

We develop fifth-order A-WENO finite-difference schemes based on the path-conservative
central-upwind method for nonconservative one-and two-dimensional hyperbolic systems of …

In this work, we consider the discretization of nonlinear hyperbolic systems in
nonconservative form with the high-order discontinuous Galerkin spectral element method …

In this paper, a new efficient, and at the same time, very simple and general class of
thermodynamically compatible finite volume schemes is introduced for the discretization of …

In this work we propose a high-order discretization of the Baer-Nunziato two-phase flow
model (Baer and Nunziato (1986)[5]) with closures for interface velocity and pressure …

We are interested in the numerical approximation of discontinuous solutions in non
conservative hyperbolic systems. An extension to second-order of a new strategy based on …

The shear shallow water model is an extension of the classical shallow water model to
include the effects of vertical shear. It is a system of six non-linear hyperbolic PDE with non …