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A numerical scheme for the one-dimensional pressureless gases system. (English) Zbl 1312.76055

Summary: We investigate the numerical approximation of the one-dimensional pressureless gases system. After briefly recalling the mathematical framework of the duality solutions introduced by F. Bouchut and F. James [Commun. Partial Differ. Equations 24, No. 11–12, 2173–2189 (1999; Zbl 0937.35098)], 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 L. Boudin [SIAM J. Math. Anal. 32, No. 1, 172–193 (2000; Zbl 0973.35057)] for the continuous model.

MSC:

76N15 Gas dynamics (general theory)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35Q31 Euler equations
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