An asymptotic preserving scheme for the relativistic Vlasov-Maxwell equations in the classical limit

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• 作者：Nicolas Crouseilles^a ; ^b ; ^{nicolas.crouseilles@inria.fr" class="auth_mail" title="E-mail the corresponding author} ; Lukas Einkemmer^c ; ^{lukas.einkemmer@uibk.ac.at" class="auth_mail" title="E-mail the corresponding author} ; Erwan Faou^d ; ^e ; ^{Erwan.Faou@inria.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Relativistic Vlasov&ndash ; Maxwell system ; Asymptotic preserving scheme ; Splitting scheme
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：209
• 期：Complete
• 页码：13-26
• 全文大小：1339 K

文摘

We consider the relativistic Vlasov–Maxwell (RVM) equations in the limit when the light velocity c$c$ goes to infinity. In this regime, the RVM system converges towards the Vlasov–Poisson system and the aim of this paper is to construct asymptotic preserving numerical schemes that are robust with respect to this limit.

Our approach relies on a time splitting approach for the RVM system employing an implicit time integrator for Maxwell’s equations in order to damp the higher and higher frequencies present in the numerical solution.

A number of numerical simulations are conducted in order to investigate the performances of our numerical scheme both in the relativistic as well as in the classical limit regime. In addition, we derive the dispersion relation of the Weibel instability for the continuous and the discretized problem.