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Journal of Scientific Computing

, Volume 77, Issue 1, pp 263–282 | Cite as

High Order Multi-dimensional Characteristics Tracing for the Incompressible Euler Equation and the Guiding-Center Vlasov Equation

  • Tao Xiong
  • Giovanni Russo
  • Jing-Mei Qiu
Article
  • 78 Downloads

Abstract

In this paper, we propose a high order characteristics tracing scheme for the two-dimensional nonlinear incompressible Euler system in vorticity stream function formulation and the guiding center Vlasov model. Such a scheme is incorporated into a semi-Lagrangian finite difference WENO framework for simulating the aforementioned model equations. This is an extension of our earlier work on high order characteristics tracing scheme for the 1D nonlinear Vlasov–Poisson system (Qiu and Russo in J Sci Comput 71:414–434, 2017). The effectiveness of the proposed scheme is demonstrated numerically by an extensive set of test cases.

Keywords

Semi-Lagrangian Characteristics tracing Finite difference WENO Incompressible Euler equation Vorticity stream function formulation Guiding-center Vlasov equation 

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Authors and Affiliations

  1. 1.School of Mathematical Sciences, Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen UniversityXiamenPeople’s Republic of China
  2. 2.Department of Mathematics and Computer ScienceUniversity of CataniaCataniaItaly
  3. 3.Department of MathematicsUniversity of DelawareNewarkUSA

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