Exponential DG methods for Vlasov equations

TL;DR

This paper introduces an exponential Discontinuous Galerkin method combined with Lawson Runge-Kutta for solving Vlasov equations, achieving high order accuracy and stability, with proven Poisson equation preservation and validated through numerical experiments.

Contribution

The paper presents a novel exponential DG method with Lawson Runge-Kutta for Vlasov equations, enabling high order accuracy and overcoming time step restrictions.

Findings

High order accuracy in time and space achieved.

Method preserves discrete Poisson equation.

Numerical results confirm good behavior and stability.

Abstract

In this work, an exponential Discontinuous Galerkin (DG) method is proposed to solve numerically Vlasov type equations. The DG method is used for space discretization which is combined exponential Lawson Runge-Kutta method for time discretization to get high order accuracy in time and space. In addition to get high order accuracy in time, the use of Lawson methods enables to overcome the stringent condition on the time step induced by the linear part of the system. Moreover, it can be proved that a discrete Poisson equation is preserved. Numerical results on Vlasov-Poisson and Vlasov Maxwell equations are presented to illustrate the good behavior of the exponential DG method.