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Numerical approximations of the 10-moment Gaussian closure

Author: Christophe Berthon
Journal: Math. Comp. 75 (2006), 1809-1831
MSC (2000): Primary 65M99, 76N15; Secondary 76P05
Published electronically: June 6, 2006
MathSciNet review: 2240636
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Abstract: We propose a numerical scheme to approximate the weak solutions of the 10-moment Gaussian closure. The moment Gaussian closure for gas dynamics is governed by a conservative hyperbolic system supplemented by entropy inequalities whose solutions satisfy positiveness of density and tensorial pressure. We consider a Suliciu-type relaxation numerical scheme to approximate the solutions. These methods are proved to satisfy all the expected positiveness properties and all the discrete entropy inequalities. The scheme is illustrated by several numerical experiments.

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Additional Information

Christophe Berthon
Affiliation: MAB, UMR 5466 CNRS, Université Bordeaux 1, 351 cours de la libération, 33400 Talence, France

Keywords: Hyperbolic system of conservation laws, Gaussian moment closure, relaxation scheme, discrete entropy inequalities
Received by editor(s): August 4, 2004
Received by editor(s) in revised form: September 13, 2005
Published electronically: June 6, 2006
Article copyright: © Copyright 2006 American Mathematical Society