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

Abstract

We consider the relativistic Vlasov--Maxwell (RVM) equations in the limit when the light velocity $c$ 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.

References in corpus (2)

• Nonlinear Kinetic Development of the Weibel Instability and the generation of electrostatic coherent structures
• Comment on "Hamiltonian splitting for the Vlasov-Maxwell equations"

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• Exponential methods for solving hyperbolic problems with application to kinetic equations
• A comparison of boundary correction methods for Strang splitting
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• ADI type preconditioners for the steady state inhomogeneous Vlasov equation