h-box methods for the approximation of hyperbolic conservation laws on irregular grids

Marsha J. Berger, Christiane Helzel, Randall J. Leveque

Research output: Contribution to journalArticlepeer-review

Abstract

We study generalizations of the high-resolution wave propagation algorithm for the approximation of hyperbolic conservation laws on irregular grids that have a time step restriction based on a reference grid cell length that can be orders of magnitude larger than the smallest grid cell arising in the discretization. This Godunov-type scheme calculates fluxes at cell interfaces by solving Riemann problems defined over boxes of a reference grid cell length h. We discuss stability and accuracy of the resulting so-called h-box methods for one-dimensional systems of conservation laws. An extension of the method for the two-dimensional case, which is based on the multidimensional wave propagation algorithm, is also described.

Original languageEnglish (US)
Pages (from-to)893-918
Number of pages26
JournalSIAM Journal on Numerical Analysis
Volume41
Issue number3
DOIs
StatePublished - 2003

Keywords

  • Accuracy
  • Conservation laws
  • Finite volume methods
  • Nonuniform grids
  • Stability

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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