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 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 …

Upwind schemes are very well adapted to advection dominated flows and have become
popular for applications involving the Euler system of equations. Recently, Riemann solver …

In this paper, certain well-known upwind schemes for hyperbolic equations are extended to
solve the two-dimensional Saint-Venant (or shallow water) equations. We consider …

This paper is concerned with the numerical approximations of Cauchy problems for one-
dimensional nonconservative hyperbolic systems. The first goal is to introduce a general …

This paper is concerned with the numerical approximation of bedload sediment transport
due to water evolution. For the hydrodynamical component we consider Shallow Water …

The goal of this paper is to construct a first-order upwind scheme for solving the system of
partial differential equations governing the one-dimensional flow of two superposed …

This paper describes the numerical solution of the 1D shallow‐water equations by a finite
volume scheme based on the Roe solver. In the first part, the 1D shallow‐water equations …

This paper deals with the numerical simulation of flows of stratified fluids through channels
with irregular geometry. Channel cross-sections are supposed to be symmetric but not …

This paper deals with the numerical difficulties related to the appearance of the so-called
wet/dry fronts that may occur during the simulation of free-surface waves in shallow fluids …