### 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 language | English (US) |
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Pages (from-to) | A861-A888 |

Journal | SIAM Journal on Scientific Computing |

Volume | 34 |

Issue number | 2 |

DOIs | |

State | Published - 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

### Cite this

*SIAM Journal on Scientific Computing*,

*34*(2), A861-A888. https://doi.org/10.1137/110829398