A numerical scheme for the one-dimensional pressureless gases system

Abstract

In this work, we investigate the numerical approximation of the one-dimensional pressureless gases system. After briefly recalling the mathematical framework of the duality solutions introduced by Bouchut and James (Comm. Partial Differential Equations 24 (1999), 2173-2189), we point out that the upwind scheme for density and momentum does not satisfy the one-sided Lipschitz (OSL) condition on the expansion rate required for the duality solutions. Then we build a diffusive scheme which allows the OSL condition to be recovered by following the strategy described by Boudin (SIAM J Math Anal 32 (2000), 172-193) for the continuous model. © 2011 Wiley Periodicals, Inc.