Kinetic and hyperbolic equations contain small scales (mean free path/time, Debye length,
relaxation or reaction time, etc.) that lead to various different asymptotic regimes, in which …

This article deals with a survey of the Newtonian fluid dynamics equations with some
historical notes and a discussion related to the solvability of fluid flows problems. On the …

In 1917, the British scientist LF Richardson made the first reported attempt to predict the
weather by solving partial differential equations numerically, by hand! It is generally …

This paper deals with the extension of some upwind schemes to hyperbolic systems of
conservation laws with source term. More precisely we give methods to get natural upwind …

Conservation laws with source terms often have steady states in which the flux gradients are
nonzero but exactly balanced by source terms. Many numerical methods (eg, fractional step …

The goal of this paper is to provide a theoretical framework allowing one to extend some
general concepts related to the numerical approximation of 1-d conservation laws to the …

This paper deals with the numerical solution of the shallow water equations in channels with
irregular geometry but with a locally rectangular cross section. This type of channel leads to …

We study a general approach to solving conservation laws of the form qt+ f (q, x) x= 0, where
the flux function f (q, x) has explicit spatial variation. Finite-volume methods are used in …

The aim of this paper is to present a numerical scheme to compute Saint-Venant equations
with a source term, due to the bottom topography, in a one-dimensional framework, which …

Hyperbolic systems often have relaxation terms that give them a partially conservative form
and that lead to a long-time behavior governed by reduced systems that are parabolic in …