Vol. 11, No. 1, 2016

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
An asymptotic-preserving scheme for systems of conservation laws with source terms on 2D unstructured meshes

Christophe Berthon, Guy Moebs, Céline Sarazin-Desbois and Rodolphe Turpault

Vol. 11 (2016), No. 1, 55–77
Abstract

In this paper, finite volume numerical schemes are developed for hyperbolic systems of conservation laws with source terms. The systems under consideration degenerate into parabolic systems in large times when the source terms become stiff. In this framework, it is crucial that the numerical schemes are asymptotic-preserving, i.e., that they degenerate accordingly. Here, an asymptotic-preserving numerical scheme is proposed for any system within the aforementioned class on 2D unstructured meshes.

This scheme is proved to be consistent and stable under a suitable CFL condition. Moreover, we show that it is also possible to prove that it preserves the set of (physically) admissible states under a geometric property on the mesh. Finally, numerical examples are given to illustrate its behavior.

Keywords
Finite volume schemes, 2D unstructured mesh, asymptotic-preserving schemes, conservation laws with source terms, positivity-preserving schemes
Mathematical Subject Classification 2010
Primary: 35L65, 65M99, 65M08
Milestones
Received: 17 January 2014
Revised: 17 March 2015
Accepted: 3 November 2015
Published: 20 January 2016
Authors
Christophe Berthon
Université de Nantes
Laboratoire de Mathématiques Jean Leray
2 rue de la Houssinière
44322 Nantes Cedex 3
France
Guy Moebs
Université de Nantes
Laboratoire de Mathématiques Jean Leray
2 rue de la Houssinière
44322 Nantes Cedex 3
France
Céline Sarazin-Desbois
Université de Nantes
Laboratoire de Mathématiques Jean Leray
2 rue de la Houssinière
44322 Nantes Cedex 3
France
Rodolphe Turpault
Bordeaux-INP
Institut de Mathématiques de Bordeaux
351 cours de la Libération
33400 Talence
France