High Order Maximum Principle Preserving Semi-Lagrangian Finite Difference WENO Schemes for the Vlasov Equation

Document Type

Article

Publication Date

9-15-2014

Department

Department of Mathematical Sciences

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.

Publisher's Statement

© 2014 Elsevier Inc.

Publication Title

Journal of Computational Physics

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