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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:354

Article

Cai, Xiaofeng¹  Guo, Wei²  Qiu, Jing-Mei¹ 

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[2] Texas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA

关键词: Semi-Lagrangian;    Discontinuous Galerkin;    Vlasov-Poisson;    Non-splitting;    Mass conservative;    Positivity-preserving;   

DOI  :  10.1016/j.jcp.2017.10.048

来源: Elsevier

【 摘 要 】

In this paper, we develop a high order semi-Lagrangian (SL) discontinuous Galerkin (DG) method for nonlinear Vlasov-Poisson (VP) simulations without operator splitting. In particular, we combine two recently developed novel techniques: one is the high order non-splitting SLDG transport method (Cai et al. (2017) [4]), and the other is the high order characteristics tracing technique proposed in Qiu and Russo (2017) [29]. The proposed method with up to third order accuracy in both space and time is locally mass conservative, free of splitting error, positivity-preserving, stable and robust for large time stepping size. The SLDG VP solver is applied to classic benchmark test problems such as Landau damping and two-stream instabilities for VP simulations. Efficiency and effectiveness of the proposed scheme is extensively tested. Tremendous CPU savings are shown by comparisons between the proposed SL DG scheme and the classical Runge-Kutta DG method. (c) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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