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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:273

Article

Xiong, Tao¹  Qiu, Jing-Mei¹  Xu, Zhengfu²  Christlieb, Andrew³ 

[1] Univ Houston, Dept Math, Houston, TX 77204 USA

[2] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA

[3] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

关键词: Semi-Lagrangian method;    Finite difference WENO scheme;    Maximum principle preserving;    Parametrized flux limiter;    Vlasov equation;   

DOI  :  10.1016/j.jcp.2014.05.033

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free