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 …

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 …

We are interested in nonlinear hyperbolic systems in nonconservative form arising in fluid
dynamics, and, for solutions containing shock waves, we investigate the convergence of …

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 standard multilayer Saint-Venant system consists in introducing fluid layers that are
advected by the interfacial velocities. As a consequence there is no mass exchanges …

Shallow-water equations are widely used to model water flow in rivers, lakes, reservoirs,
coastal areas, and other situations in which the water depth is much smaller than the …

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 …