Multiscale schemes for the BGK-Vlasov-Poisson system in the quasi-neutral and fluid limits. Stability analysis and first order schemes.

Nicolas Crouseilles 1 Giacomo Dimarco 2 Marie-Hélène Vignal 3
1 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
2 Department of Mathematics [Ferrara]
3 IMT - Institut de Mathématiques de Toulouse UMR5219
Abstract : This paper deals with the development and the analysis of asymptotic stable and consistent schemes in the joint quasi-neutral and fluid limits of the collisional Vlasov Poisson system. In these limits, the classical explicit schemes suffer from time step restrictions due to the small plasma period and Knudsen number. To solve this problem, we propose a new scheme stable for choices of time steps independent from the small scales dynamics and with comparable computational cost with respect to standard explicit schemes. In addition, this scheme reduces automatically to consistent discretizations of the underlying asymptotic systems. In this first work on this subject, we propose a first order in time scheme and we perform a relative linear stability analysis to deal with such problems. The framework we propose permits to extend this approach to high order schemes in the next future. We finally show the capability of the method in dealing with small scales through numerical experiments.
Keywords : quasi-neutral limit multiscale Collisional Vlasov-Poisson system asymptotic preserving schemes stability analysis fluid-dynamic limit
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Article dans une revue
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2016, 14 (1), pp.65-95. 〈10.1137/140991558〉
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Nicolas Crouseilles, Giacomo Dimarco, Marie-Hélène Vignal. Multiscale schemes for the BGK-Vlasov-Poisson system in the quasi-neutral and fluid limits. Stability analysis and first order schemes.. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2016, 14 (1), pp.65-95. 〈10.1137/140991558〉. 〈hal-01090676〉

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