A semi-Lagrangian finite difference WENO scheme for scalar nonlinear conservation laws

JOURNAL OF COMPUTATIONAL PHYSICS

卷:322

Article

Huang, Chieh-Sen¹  Arbogast, Todd²  Hung, Chen-Hui³ 

[1] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan

[2] Univ Texas Austin, Inst Computat Engn & Sci, 201 EAST 24th St,Stop C0200, Austin, TX 78712 USA

[3] Air Force Acad, Dept Math & Phys Sci, Sisou 1,Jieshou W Rd, Kaohsiung 82047, Taiwan

关键词: Hyperbolic;    Semi-Lagrangian;    WENO reconstruction;    Eulerian-Lagrangian;    Traceline;    Locally frozen;   

DOI  :  10.1016/j.jcp.2016.06.027

来源: Elsevier

【 摘 要 】

For a nonlinear scalar conservation law in one-space dimension, we develop a locally conservative semi-Lagrangian finite difference scheme based on weighted essentially non-oscillatory reconstructions (SL-WENO). This scheme has the advantages of both WENO and semi-Lagrangian schemes. It is a locally mass conservative finite difference scheme, it is formally high-order accurate in space, it has small time truncation error, and it is essentially non-oscillatory. The scheme is nearly free of a CFL time step stability restriction for linear problems, and it has a relaxed CFL condition for nonlinear problems. The scheme can be considered as an extension of the SL-WENO scheme of Qiu and Shu (2011) [2] developed for linear problems. The new scheme is based on a standard sliding average formulation with the flux function defined using WENO reconstructions of (semi-Lagrangian) characteristic tracings of grid points. To handle nonlinear problems, we use an approximate, locally frozen trace velocity and a flux correction step. A special two-stage WENO reconstruction procedure is developed that is biased to the upstream direction. A Strang splitting algorithm is used for higher-dimensional problems. Numerical results are provided to illustrate the performance of the scheme and verify its formal accuracy. Included are applications to the Vlasov-Poisson and guiding-center models of plasma flow. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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