A moving mesh WENO method based on exponential polynomials for one-dimensional conservation laws

Andrew Christlieb, Wei Guo, Yan Jiang, Hyoseon Yang

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

In the article [Yang et al. (2012) [37]], the authors have developed a high order moving mesh WENO method for one-dimensional (1D) hyperbolic conservation laws, which is shown to be effective in resolving shocks and other complex solution structures. In this paper, in the light of the similar moving mesh technique, we develop a novel WENO scheme with non-polynomial bases, in particular, the exponential bases to further improve the performance of WENO schemes for solving 1D conservation laws. Furthermore, we modify the original moving mesh technique by developing a new monitor function as well as a different mesh smoothing strategy. A collection of numerical examples is presented to demonstrate high order accuracy and robustness of the method in capturing smooth and non-smooth solutions including the strong δ shock arising from the weakly hyperbolic pressureless Euler equations.

Original languageEnglish
Pages (from-to)334-354
Number of pages21
JournalJournal of Computational Physics
Volume380
DOIs
StatePublished - Mar 1 2019

Keywords

  • Conservation laws
  • Exponential polynomials
  • Finite difference
  • Moving mesh
  • WENO

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