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

• Published in: Journal of computational physics Vol. 354; pp. 529 - 551
• Main Authors: Cai, Xiaofeng, Guo, Wei, Qiu, Jing-Mei
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.02.2018; Elsevier Science Ltd
• Subjects: Computational physics; Discontinuous Galerkin; Galerkin method; Landau damping; Mass conservative; Non-splitting; Numerical analysis; Positivity-preserving; Probability distribution; Runge-Kutta method; Semi-Lagrangian; Simulation; Splitting; Vlasov–Poisson; Non-splitting; Discontinuous Galerkin; Positivity-preserving; Semi-Lagrangian; Vlasov–Poisson; Mass conservative
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2017.10.048

•The semi-Lagrangian discontinuous Galerkin (SLDG) method for the Vlasov–Poisson (VP) system has several desired properties.•It is locally mass conservative, highly accurate, free of splitting error and allows for extra large time stepping size.•To the best of authors' knowledge, this is the first SLDG scheme for VP simulations that is able to attain all these properties.•The method is applied to classic benchmark VP test problems, with effectiveness and efficiency showcased.•Tremendous CPU savings are observed, when compared with those from the classical Runge–Kutta DG method. 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.