High order maximum principle preserving semi-Lagrangian finite difference WENO schemes for the Vlasov equation

Abstract

In this paper, we propose the parametrized maximum principle preserving (MPP) flux limiter, originally developed in [37], to the semi-Lagrangian finite difference weighted essentially non-oscillatory scheme for solving the Vlasov equation. The MPP flux limiter is proved to maintain up to fourth order accuracy for the semi-Lagrangian finite difference scheme without any time step restriction. Numerical studies on the Vlasov-Poisson system demonstrate the performance of the proposed method and its ability in preserving the positivity of the probability distribution function while maintaining the high order accuracy. © 2014 Elsevier Inc