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

摘要

In this paper, we develop a high order semi-Lagrangian (SL) discontinuousGalerkin (DG) method for nonlinear Vlasov-Poisson (VP) simulations withoutoperator splitting. In particular, we combine two recently developed noveltechniques: one is the high order non-splitting SLDG transport method [Cai, etal., J Sci Comput, 2017], and the other is the high order characteristicstracing technique proposed in [Qiu and Russo, J Sci Comput, 2017]. The proposedmethod with up to third order accuracy in both space and time is locally massconservative, free of splitting error, positivity-preserving, stable and robustfor large time stepping size. The SLDG VP solver is applied to classicbenchmark test problems such as Landau damping and two-stream instabilities forVP simulations. Efficiency and effectiveness of the proposed scheme isextensively tested. Tremendous CPU savings are shown by comparisons between theproposed SL DG scheme and the classical Runge-Kutta DG method.