Journal
KINETIC AND RELATED MODELS
Volume 5, Issue 4, Pages 787-816Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/krm.2012.5.787
Keywords
Vlasov equation; BGK equation; Euler equation; Chapman-Enskog expansion; asymptotic preserving schemes; micro-macro decomposition; particles method
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Funding
- ERC GEOPARDI
- FUSION INRIA Large scale initiative
- Federation de Recherche sur la Fusion Magnetique
- ANR project LODIQUAS
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This work is devoted to the numerical simulation of the Vlasov equation in the fluid limit using particles. To that purpose, we first perform a micro-macro decomposition as in [3] where asymptotic preserving schemes have been derived in the fluid limit. In [3], a uniform grid was used to approximate both the micro and the macro part of the full distribution function. Here, we modify this approach by using 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 fluid regime 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 fluid regime.
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