Moving mesh methods with locally varying time steps

Zhijun Tan, Zhengru Zhang, Yunqing Huang, Tao TANG*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

55 Citations (Scopus)

Abstract

The time steps associated with moving mesh methods are proportional to the smallest mesh size in space and as a result they are very small at each time level. For some practical problems, the physical phenomena develop dynamically singular or nearly singular solutions in fairly localized regions, and therefore the smallest time step at each time level occurs only in these localized regions. In this work, we will develop a local time stepping algorithm for the moving mesh methods. The principal idea will be demonstrated by investigating the nonlinear hyperbolic conservation laws. Numerical experiments are carried out to demonstrate the efficiency and robustness of the proposed methods.

Original languageEnglish
Pages (from-to)347-367
Number of pages21
JournalJournal of Computational Physics
Volume200
Issue number1
DOIs
Publication statusPublished - 10 Oct 2004

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Finite volume method
  • Hyperbolic conservation laws
  • Local time stepping
  • Moving mesh method

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