This book is devoted to finite volume methods for hyperbolic systems of conservation laws. It
differs from previous expositions on the subject in that the accent is put on the development …

We present a relaxation system for ideal magnetohydrodynamics (MHD) that is an extension
of the Suliciu relaxation system for the Euler equations of gas dynamics. From it one can …

This article focuses on the design of semi-implicit schemes that are fully well-balanced for
the one-dimensional shallow water equations, that is, schemes that preserve all smooth …

Entropy conservation and stability of numerical methods in gas dynamics have received
much interest. Entropy conservative numerical fluxes can be used as ingredients in two …

We propose large time step and asymptotic preserving schemes for the gas dynamics
equations with external forces and friction terms. By asymptotic preserving, we mean that the …

Well-balanced or asymptotic preserving schemes are receiving an increasing amount of
interest. This paper gives a precise setting for studying both properties in the case of Euler …

We present a relaxation scheme for approximating the entropy dissipating weak solutions of
the Baer–Nunziato two-phase flow model. This relaxation scheme is straightforwardly …

This book focuses on the interplay between Eulerian and Lagrangian conservation laws for
systems that admit physical motivation and originate from continuum mechanics. Ultimately …

We construct an approximate Riemann solver for the isentropic Baer− Nunziato two-phase
flow model, that is able to cope with arbitrarily small values of the statistical phase fractions …

We propose a numerical scheme to approximate the weak solutions of the 10-moment
Gaussian closure. The moment Gaussian closure for gas dynamics is governed by a …