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

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, 361005, Fujian, People’s Republic of China

    Tao Xiong

  2. Department of Mathematics and Computer Science, University of Catania, 95125, Catania, Italy

    Giovanni Russo

  3. Department of Mathematics, University of Delaware, Newark, DE, 19716, USA

    Jing-Mei Qiu

Authors
  1. Tao Xiong
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  2. Giovanni Russo
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  3. Jing-Mei Qiu
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Corresponding author

Correspondence to Jing-Mei Qiu.

Additional information

T. Xiong: Research supported by NSF Grant of Fujian Province 2016J05022, NSFC Grant 11601455, NSAF Grant U1630247, the Fundamental Research Funds for the Central Universities No. 20720160009, and the Marie Skłodowska-Curie Individual Fellowships H2020-MSCA-IF-2014 of the European Commision under the project HNSKMAP 654175.

J.-M. Qiu: Research supported by NSF Grant NSF-DMS-1522777 and Air Force Office of Scientific Computing FA9550-12-0318.

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Xiong, T., Russo, G. & Qiu, JM. High Order Multi-dimensional Characteristics Tracing for the Incompressible Euler Equation and the Guiding-Center Vlasov Equation. J Sci Comput 77, 263–282 (2018). https://doi.org/10.1007/s10915-018-0705-y

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  • DOI: https://doi.org/10.1007/s10915-018-0705-y

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