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

TL;DR

This paper develops an asymptotic preserving numerical scheme for the relativistic Vlasov--Maxwell equations that remains stable and accurate as the light velocity tends to infinity, effectively bridging relativistic and classical plasma models.

Contribution

The paper introduces a novel time splitting scheme with implicit Maxwell integration that is robust in the classical limit, ensuring accurate simulations across regimes.

Findings

Scheme effectively captures classical limit behavior

Numerical simulations demonstrate robustness in relativistic and non-relativistic regimes

Dispersion relation analysis of Weibel instability for continuous and discrete cases

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.