A high order semi-Lagrangian discontinuous Galerkin method for Vlasov-Poisson simulations without operator splitting

TL;DR

This paper introduces a high-order semi-Lagrangian discontinuous Galerkin method for Vlasov-Poisson simulations that avoids operator splitting, offering improved accuracy, stability, and computational efficiency for plasma physics problems.

Contribution

It combines two advanced techniques to develop a high-order, non-splitting, mass-conservative, positivity-preserving DG method for Vlasov-Poisson simulations, eliminating splitting errors.

Findings

Achieves up to third-order accuracy in space and time.

Demonstrates significant CPU savings over classical methods.

Successfully applies to benchmark plasma problems like Landau damping.

Abstract

In this paper, we develop a high order semi-Lagrangian (SL) discontinuous Galerkin (DG) method for nonlinear Vlasov-Poisson (VP) simulations without operator splitting. In particular, we combine two recently developed novel techniques: one is the high order non-splitting SLDG transport method [Cai, et al., J Sci Comput, 2017], and the other is the high order characteristics tracing technique proposed in [Qiu and Russo, J Sci Comput, 2017]. The proposed method with up to third order accuracy in both space and time is locally mass conservative, free of splitting error, positivity-preserving, stable and robust for large time stepping size. The SLDG VP solver is applied to classic benchmark test problems such as Landau damping and two-stream instabilities for VP simulations. Efficiency and effectiveness of the proposed scheme is extensively tested. Tremendous CPU savings are shown by comparisons between the proposed SL DG scheme and the classical Runge-Kutta DG method.