Multiscale schemes for the BGK-Vlasov-Poisson system in the quasi-neutral and fluid limits. Stability analysis and first order schemes. - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal Year : 2016

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

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.
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Dates and versions

hal-01090676 , version 1 (10-12-2014)

Identifiers

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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, 2016, 14 (1), pp.65-95. ⟨10.1137/140991558⟩. ⟨hal-01090676⟩
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