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 …

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 …

In some previous works, the authors have introduced a strategy to develop well-balanced
high-order numerical methods for nonconservative hyperbolic systems in the framework of …

In this article, we propose a new class of finite volume schemes of arbitrary accuracy in
space and time for systems of hyperbolic balance laws with stiff source terms. The new class …

This paper is concerned with the development of high order methods for the numerical
approximation of one-dimensional nonconservative hyperbolic systems. In particular, we are …

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 …

In this chapter we describe a general methodology for developing high-order well-balanced
schemes for hyperbolic system with nonconservative products and/or source terms. We …

The goal of this paper is to generalize the hydrostatic reconstruction technique introduced in
Ref. 2 for the shallow water system to more general hyperbolic systems with source term …