A kinetic scheme for the Saint-Venant system with a source term
type: Item
instance of: scholarly article
title: A kinetic scheme for the Saint-Venant system with a source term
zbMATH Open document ID: 1008.65066
published in: Calcolo
publication date: 2002-12-17T00:00:00Z
review text: The aim of this paper is to present a numerical scheme to compute Saint-Venant equations with source term, due to the bottom topography, in a one-dimensional framework, which satisfies the following theoretical properties: it preserves the steady state of still water, satisfies an entropy inequality, preserves the non-negativity of the height of water and remains stable with a discontinuous bottom. This is achieved by means of a kinetic approach to the system, which is the departing point of the method developed here. In this context, the authors use a natural description of the microscopic behavior of the system to define numerical fluxes at the interfaces of an unstructured mesh. The concept of cell-centered conservative quantities (as usual in the finite volume method) and upwind interfacial sources as advocated by several authors is also used. Analytically and also by means of numerical results, it is shown that the above properties are satisfied.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 76M12
Mathematics Subject Classification ID: 76M20
zbMATH DE Number: 1846809
zbMATH Keywords: shallow-water equations
zbMATH Keywords: hyperbolic systems of conservation laws
zbMATH Keywords: finite-difference schemes
zbMATH Keywords: volume method
author: Ben{ôı}t Perthame
author: Chiara Simeoni
reviewed by: Violeta A. Kostova
MaRDI profile type: Publication
full work available at URL: s10092-001-8181-3
OpenAlex ID: W2018277869
DOI: 10.1007/S10092-001-8181-3
description: scientific article; zbMATH DE number 1846809