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On the gain of regularity for the positive part of Boltzmann collision operator associated with soft-potentials
December  2012, 5(4): 787-816. doi: 10.3934/krm.2012.5.787

## Kinetic/fluid micro-macro numerical schemes for Vlasov-Poisson-BGK equation using particles

 1 INRIA-Nancy Grand Est, CALVI Project, and IRMA, Université de Strasbourg, 67084, STRASBOURG, France 2 INRIA-Rennes Bretagne Atlantique, IPSO Project, and IRMAR (Université de Rennes 1), 35042 RENNES, France 3 CNRS and IRMAR (Université de Rennes 1), and INRIA-Rennes Bretagne Atlantique, IPSO Project, 35042 RENNES, France

Received  April 2012 Revised  June 2012 Published  November 2012

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.
Citation: Anaïs Crestetto, Nicolas Crouseilles, Mohammed Lemou. Kinetic/fluid micro-macro numerical schemes for Vlasov-Poisson-BGK equation using particles. Kinetic & Related Models, 2012, 5 (4) : 787-816. doi: 10.3934/krm.2012.5.787
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##### References:
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