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 language | English (US) |
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Pages (from-to) | 893-918 |
Number of pages | 26 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 41 |
Issue number | 3 |
DOIs | |
State | Published - 2003 |
Keywords
- Accuracy
- Conservation laws
- Finite volume methods
- Nonuniform grids
- Stability
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics