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 Qiu

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)1111-1134
Number of pages24
JournalJournal of Scientific Computing
Volume79
Issue number2
DOIs
StatePublished - May 15 2019

Keywords

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

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