Conservative discontinuous Galerkin/Hermite Spectral Method for the Vlasov-Poisson System

TL;DR

This paper introduces a conservative discontinuous Galerkin method using Hermite polynomials for the Vlasov-Poisson system, achieving high accuracy and conservation of mass and energy, verified through numerical simulations.

Contribution

It presents a novel DG scheme that is systematically accurate and conserves key physical quantities for the Vlasov-Poisson system.

Findings

Scheme achieves high order accuracy.

Mass and energy are conserved in simulations.

Numerical results verify theoretical properties.

Abstract

We propose a class of conservative discontinuous Galerkin methods for the Vlasov-Poisson system written as a hyperbolic system using Hermite polynomials in the velocity variable. These schemes are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in general are hard to achieve within other numerical method frameworks for simulating the Vlasov-Poisson system. The proposed scheme employs discontinuous Galerkin discretization for both the Vlasov and the Poisson equations, resulting in a consistent description of the distribution function and electric field. Numerical simulations are performed to verify the order of accuracy and conservation properties.