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

详细信息    查看全文

• 作者：Chieh-Sen Huang^a ; ¹ ; ^{huangcs@math.nsysu.edu.tw" class="auth_mail" title="E-mail the corresponding author} ; Todd Arbogast^b ; ² ; ^{arbogast@ices.utexas.edu" class="auth_mail" title="E-mail the corresponding author} ; Chen-Hui Hung^c ; ^{hungch@math.nsysu.edu.tw" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Hyperbolic ; Semi-Lagrangian ; WENO reconstruction ; Eulerian&ndash ; Lagrangian ; Traceline ; Locally frozen
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：1 October 2016
• 年：2016
• 卷：322
• 期：Complete
• 页码：559-585
• 全文大小：10946 K

文摘

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.