Asymptotic-Preserving scheme based on a Finite Volume/Particle-In-Cell coupling for Boltzmann- BGK-like equations in the diffusion scaling

Anaïs Crestetto (1) , Nicolas Crouseilles (2, 3) , Mohammed Lemou (2, 3)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 IPSO - Invariant Preserving SOlvers
3 IRMAR - Institut de Recherche Mathématique de Rennes

This work is devoted to the numerical simulation of the collisional Vlasov equation in the diffusion limit using particles. To that purpose, we use a micro-macro decomposition technique introduced by Bennoune, Lemou and Mieussens. Whereas a uniform grid was used to approximate both the micro and the macro part of the full distribution function in their article, we use here a particle approximation for the kinetic (micro) part, the fluid (macro) part being always discretized by standard finite volume schemes. There are many advantages in doing so: (i) the so-obtained scheme presents a much less level of noise compared to the standard particle method; (ii) the computational cost of the micro-macro model is reduced in the diffusion limit since a small number of particles is needed for the micro part; (iii) the scheme is asymptotic preserving in the sense that it is consistent with the kinetic equation in the rarefied regime and it degenerates into a uniformly (with respect to the Knudsen number) consistent (and deterministic) approximation of the limiting equation in the diffusion regime.

Domaines: Analyse numérique [math.NA]

Anaïs Crestetto, Nicolas Crouseilles, Mohammed Lemou. Asymptotic-Preserving scheme based on a Finite Volume/Particle-In-Cell coupling for Boltzmann- BGK-like equations in the diffusion scaling. Finite Volumes for Complex Applications VII, Jun 2014, Berlin, Germany. p. 827, ⟨10.1007/978-3-319-05591-6_83⟩. ⟨hal-01015936⟩