A simplified h-box method for embedded boundary grids

Marsha Berger, Christiane Helzel

Research output: Contribution to journalArticle

Abstract

We present a simplified h-box method for integrating time-dependent conservation laws on embedded boundary grids using an explicit finite volume scheme. By using a method of lines approach with a strong stability preserving Runge-Kutta method in time, the complexity of our previously introduced h-box method is greatly reduced. A stable, accurate, and conservative approximation is obtained by constructing a finite volume method where the numerical fluxes satisfy a certain cancellation property. For a model problem in one space dimension using appropriate limiting strategies, the resulting method is shown to be total variation diminishing. In two space dimensions, stability is maintained by using rotated h-boxes as introduced in previous work [M. J. Berger and R. J. LeVeque, Comput. Systems Engrg., 1 (1990), pp. 305-311; C. Helzel, M. J. Berger, and R. J. LeVeque, SIAM J. Sci. Comput., 26 (2005), pp. 785-809], but in the new formulation, h-box gradients are taken solely from the underlying Cartesian grid, which also reduces the computational cost.

Original languageEnglish (US)
Pages (from-to)A861-A888
JournalSIAM Journal on Scientific Computing
Volume34
Issue number2
DOIs
StatePublished - May 28 2012

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Keywords

  • Cartesian grid cut cell method
  • Conservation laws
  • Finite volume

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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