Highly efficient energy-conserving moment method for the multi-dimensional Vlasov-Maxwell system

Abstract

This paper concerns an energy-conserving numerical method to solve the multi-dimensional Vlasov-Maxwell (VM) system based on the regularized moment method proposed in [7]. The globally hyperbolic moment system is deduced for the VM system under the framework of Hermite expansions, where the expansion center and the scaling factor are set as the macroscopic velocity and the local temperature, respectively. Thus, the effect of the Lorentz force term can be reduced into several ODEs regarding the macroscopic velocity and the higher-order moment coefficients, which can significantly reduce the computational cost of the whole system. An energy-conserving numerical scheme is proposed to solve the moment equations and Maxwell's equations, where only a small linear system needs to be solved implicitly. Benchmark examples such as Landau damping, two-stream instability, Weibel instability, and two-dimensional Orszag-Tang vortex problem are studied to validate the efficiency and excellent energy-preserving property of the numerical scheme.