Journal of Scientific Computing

, Volume 79, Issue 2, pp 1111–1134 | Cite as

A High Order Semi-Lagrangian Discontinuous Galerkin Method for the Two-Dimensional Incompressible Euler Equations and the Guiding Center Vlasov Model Without Operator Splitting

  • Xiaofeng Cai
  • Wei Guo
  • Jing-Mei QiuEmail author


In this paper, we generalize a high order semi-Lagrangian (SL) discontinuous Galerkin (DG) method for multi-dimensional linear transport equations without operator splitting developed in Cai et al. (J Sci Comput 73(2–3):514–542, 2017) to the 2D time dependent incompressible Euler equations in the vorticity-stream function formulation and the guiding center Vlasov model. We adopt a local DG method for Poisson’s equation of these models. For tracing the characteristics, we adopt a high order characteristics tracing mechanism based on a prediction-correction technique. The SLDG with large time-stepping size might be subject to extreme distortion of upstream cells. To avoid this problem, we propose a novel adaptive time-stepping strategy by controlling the relative deviation of areas of upstream cells.


Semi-Lagrangian Discontinuous Galerkin Guiding center Vlasov model Incompressible Euler equations Non-splitting Mass conservative Adaptive time-stepping method 



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Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  2. 2.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA

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