Finite volume methods are a class of discretization schemes resulting from the
decomposition of a problem domain into nonoverlapping control volumes. Degrees of …

We consider the Saint-Venant system for shallow water flows, with nonflat bottom. It is a
hyperbolic system of conservation laws that approximately describes various geophysical …

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 …

A family of Godunov-type central-upwind schemes for the Saint-Venant system of shallow
water equations has been first introduced in A. Kurganov and D. Levy, Central-upwind …

Shallow water equations with a non-flat bottom topography have been widely used to model
flows in rivers and coastal areas. An important difficulty arising in these simulations is the …

We present one-and two-dimensional central-upwind schemes for approximating solutions
of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant …

Many geophysical flows are merely perturbations of some fundamental equilibrium state. If a
numerical scheme shall capture such flows efficiently, it should be able to preserve the …

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 …

We present a finite volume scheme for solving shallow water equations with source term due
to the bottom topography. The scheme has the following properties: it is high-order accurate …

We consider the solution of the Saint-Venant equations with topographic source terms on 2D
unstructured meshes by a finite volume approach. We first present a stable and positivity …