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

TL;DR

This paper introduces an energy-conserving numerical scheme based on a regularized moment method for efficiently solving the multi-dimensional Vlasov-Maxwell system, reducing computational cost while preserving energy.

Contribution

The paper develops a globally hyperbolic moment system using Hermite expansions with adaptive centers, and proposes an energy-conserving scheme that simplifies computations to linear equations.

Findings

The scheme accurately captures plasma instabilities.

It significantly reduces computational cost.

It preserves energy over long simulations.

Abstract

We present an energy-conserving numerical scheme to solve the Vlasov-Maxwell (VM) system based on the regularized moment method proposed in [Z. Cai, Y. Fan, and R. Li. CPAM, 2014]. The globally hyperbolic moment system is deduced for the multi-dimensional VM system under the framework of the Hermite expansions, where the expansion center and the scaling factor are set as the macroscopic velocity and local temperature, respectively. Thus, the effect of the Lorentz force term could be reduced into several ODEs about the macroscopic velocity and the moment coefficients of higher order, which could significantly reduce the computational cost of the whole system. An energy-conserving numerical scheme is proposed to solve the moment equations and the Maxwell equations, where only a linear equation system needs to be solved. Several numerical examples such as the two-stream instability, Weibel instability, and the two-dimensional Orszag Tang vortex problem are studied to validate the efficiency and excellent energy-preserving property of the numerical scheme.