Late-time/stiff-relaxation asymptotic-preserving approximations of hyperbolic equations
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- by Christophe Berthon, Philippe G. LeFloch and Rodolphe Turpault PDF
- Math. Comp. 82 (2013), 831-860 Request permission
Abstract:
We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff relaxation terms. First, we introduce a Chapman-Enskog-type asymptotic expansion and derive an effective system of equations describing the late-time/stiff-relaxation singular limit. The structure of this new system is discussed and the role of a mathematical entropy is emphasized. Second, we propose a new finite volume discretization which, in late-time asymptotics, allows us to recover a discrete version of the same effective asymptotic system. This is achieved provided we suitably discretize the relaxation term in a way that depends on a matrix-valued free-parameter, chosen so that the desired asymptotic behavior is obtained. Our results are illustrated with several models of interest in continuum physics, and numerical experiments demonstrate the relevance of the proposed theory and numerical strategy.References
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Additional Information
- Christophe Berthon
- Affiliation: Université de Nantes, Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, 2 rue de la Houssinière, BP 92208, 44322 Nantes, France
- MR Author ID: 654277
- Email: Christophe.Berthon@math.univ-nantes.fr
- Philippe G. LeFloch
- Affiliation: Laboratoire Jacques-Louis Lions, Centre National de la Recherche Scientifique, Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris, France
- Email: contact@philippelefloch.org
- Rodolphe Turpault
- Affiliation: Université de Nantes, Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, 2 rue de la Houssinière, BP 92208, 44322 Nantes, France
- Email: Rodolphe.Turpault@univ-nantes.fr
- Received by editor(s): November 15, 2010
- Received by editor(s) in revised form: March 10, 2011, and September 18, 2011
- Published electronically: December 13, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 82 (2013), 831-860
- MSC (2010): Primary 35L65, 65M99
- DOI: https://doi.org/10.1090/S0025-5718-2012-02666-4
- MathSciNet review: 3008840