Diffusion Limit of the Lorentz Model: Asymptotic Preserving Schemes
CEA/DAM Ile de France, BP 12, 91680
Bruyères-Le-Châtel, France. Christophe.Buet@cea.fr.
2 Laboratoire MAPMO, UMR 6628, Université d'Orléans, 45067 Orléans, France. Stephane.Cordier@univ-orleans.fr.
3 Laboratoire d'Analyse Numérique, UMR 7598, Université Pierre et Marie Curie, BP 187, 75252 Paris Cedex 05, France. email@example.com. firstname.lastname@example.org.
Revised: 1 March 2002
This paper deals with the diffusion limit of a kinetic equation where the collisions are modeled by a Lorentz type operator. The main aim is to construct a discrete scheme to approximate this equation which gives for any value of the Knudsen number, and in particular at the diffusive limit, the right discrete diffusion equation with the same value of the diffusion coefficient as in the continuous case. We are also naturally interested with a discretization which can be used with few velocity discretization points, in order to reduce the cost of computation.
Mathematics Subject Classification: 82C70 / 35B40 / 65N06
Key words: Hilbert expansion / diffusion limit.
© EDP Sciences, SMAI, 2002