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arXiv · 1401.0076

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

Tao Xiong·Jing-Mei Qiu·Zhengfu Xu·Andrew Christlieb
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Abstract

In this paper, we propose the parametrized maximum principle preserving (MPP) flux limiter, originally developed in [Z. Xu, Math. Comp., (2013), in press], 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.

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Tao Xiong, Jing-Mei Qiu, Zhengfu Xu, Andrew Christlieb. 2013-12-31. High Order Maximum Principle Preserving Semi-Lagrangian Finite Difference WENO schemes for the Vlasov Equation. https://doi.org/10.1016/j.jcp.2014.05.033

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