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Diffusion Limit of the Lorentz Model: Asymptotic Preserving Schemes

Published online by Cambridge University Press:  15 September 2002

Christophe Buet ,
Stéphane Cordier ,
Brigitte Lucquin-Desreux  and
Simona Mancini
Christophe Buet
Affiliation:
CEA/DAM Ile de France, BP 12, 91680 Bruyères-Le-Châtel, France. Christophe.Buet@cea.fr.
Stéphane Cordier
Affiliation:
Laboratoire MAPMO, UMR 6628, Université d'Orléans, 45067 Orléans, France. Stephane.Cordier@univ-orleans.fr.
Brigitte Lucquin-Desreux
Affiliation:
Laboratoire d'Analyse Numérique, UMR 7598, Université Pierre et Marie Curie, BP 187, 75252 Paris Cedex 05, France. lucquin@ann.jussieu.fr. smancini@ann.jussieu.fr.
Simona Mancini
Affiliation:
Laboratoire d'Analyse Numérique, UMR 7598, Université Pierre et Marie Curie, BP 187, 75252 Paris Cedex 05, France. lucquin@ann.jussieu.fr. smancini@ann.jussieu.fr.
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Abstract

This paper deals with the diffusion limit of a kinetic equation where thecollisions are modeled by a Lorentz type operator. The main aim is to construct adiscrete scheme to approximate this equation which gives for any value of theKnudsen number, and in particular at the diffusive limit, the right discretediffusion equation with the same value of the diffusion coefficient as in thecontinuous case. We are also naturally interested with a discretization whichcan be used with few velocity discretization points, in order to reduce the cost ofcomputation.

Keywords

Hilbert expansiondiffusion limit.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 4 , July 2002 , pp. 631 - 655
Copyright
© EDP Sciences, SMAI, 2002

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