We present the asymptotic transitions from microscopic to macroscopic physics, their
computational challenges and the asymptotic-preserving (AP) strategies to compute …

A non-negativity preserving and well-balanced scheme that exactly preserves all the smooth
steady states of the shallow water system, including the moving ones, is proposed. In …

We are interested in the numerical approximation of the solutions of the compressible seven-
equation two-phase flow model. We propose a numerical srategy based on the derivation of …

We consider the shallow-water equations with Manning friction or topography, as well as a
combination of both these source terms. The main purpose of this work concerns the …

This work is devoted to the derivation of a fully well-balanced numerical scheme for the well-
known shallow-water model. During the last two decades, several well-balanced strategies …

In this paper, we develop a fully conservative, positivity-preserving, and entropy-bounded
discontinuous Galerkin scheme for simulating the multicomponent, chemically reacting …

This paper describes a numerical discretization of the compressible Euler equations with a
gravitational potential. A pertinent feature of the solutions to these inhomogeneous …

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 …

L'objectif de ce travail est le développement d'un modèle et d'une méthode numérique
adaptés à la simulation duruissellement d'eau de pluie sur des surfaces agricoles. Pour …

The main goal of this work is the resolution of the two-dimensional shallow water equations
of water–sediment mixture coupled to the transport diffusion equation for the total sediment …