TITLE

An asymptotic preserving scheme for the Kac model of the Boltzmann equation in the diffusion limit

AUTHOR(S)
Bennoune, Mounir; Lemou, Mohammed; Mieussens, Luc
PUB. DATE
November 2009
SOURCE
Continuum Mechanics & Thermodynamics;Nov2009, Vol. 21 Issue 5, p401
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this article, we propose a numerical scheme to solve the Kac model of the Boltzmann equation for multiscale rarefied gas dynamics. Formally, this scheme is shown to be uniformly stable with respect to the Knudsen number, consistent with the fluid-diffusion limit for small Knudsen numbers, and with the Kac equation in the kinetic regime. Our approach is based on the micro�macro decomposition which leads to an equivalent formulation of the Kac model that couples a kinetic equation with macroscopic ones. This method is validated with various test cases and compared to other standard methods.
ACCESSION #
45547893

 

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