H-Box Methods for the Approximation of Hyperbolic Conservation Laws on Irregular Grids

Authors:
Marsha J. Berger;Christiane Helzel;Randall J. LeVeque
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2003

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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.