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Analysis of an Asymptotic Preserving Scheme for RelaxationSystems∗

Published online by Cambridge University Press:  15 January 2013

Francis Filbet  and
Amélie Rambaud
Francis Filbet
Affiliation:
Université de Lyon, UMR5208, Institut Camille Jordan, Université Claude Bernard Lyon 1 43 boulevard 11 novembre 1918, 69622 Villeurbanne Cedex, France.. filbet@math.univ-lyon1.fr; rambaud@math.univ-lyon1.fr
Amélie Rambaud
Affiliation:
Université de Lyon, UMR5208, Institut Camille Jordan, Université Claude Bernard Lyon 1 43 boulevard 11 novembre 1918, 69622 Villeurbanne Cedex, France.. filbet@math.univ-lyon1.fr; rambaud@math.univ-lyon1.fr
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Abstract

We consider an asymptotic preserving numerical scheme initially proposed by F. Filbet andS. Jin [J. Comput. Phys. 229 (2010)] and G. Dimarco and L.Pareschi [SIAM J. Numer. Anal. 49 (2011) 2057–2077] in thecontext of nonlinear and stiff kinetic equations. Here, we propose a convergence analysisof such a scheme for the approximation of a system of transport equations with a nonlinearsource term, for which the asymptotic limit is given by a conservation law. We investigatethe convergence of the approximate solution (uεh, vεh) to a nonlinear relaxation system, whereε > 0 is a physical parameter andh represents the discretization parameter. Uniform convergence withrespect to ε and h is proved and error estimates arealso obtained. Finally, several numerical tests are performed to illustrate the accuracyand efficiency of such a scheme.

Keywords

Hyperbolic equations with relaxationfluid dynamic limitasymptotic-preserving schemes
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 2 , March 2013 , pp. 609 - 633
Copyright
© EDP Sciences, SMAI, 2013

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