A wave propagation method for three-dimensional hyperbolic conservation laws

A class of wave propagation algorithms for three-dimensional conservation l aws and other hyperbolic systems is developed. These unsplit finite-volume methods are based on solving one-dimensional Riemann problems at the cell i nterfaces and applying flux-limiter functions to suppress oscillations aris ing from second-derivative terms. Waves emanating from the Riemann problem are further split by solving Riemann problems in the transverse directions to model cross-derivative terms. With proper upwinding, a method that is st able for Courant numbers up to 1 can be developed. The stability theory for three-dimensional algorithms is found to be more subtle than in two dimens ions and is studied in detail. In particular we find that some methods whic h are unconditionally unstable when no limiter is applied are (apparently) stabilized by the limiter function and produce good looking results. Severa l computations using the Euler equations are presented including blast wave and complex shock/vorticity problems. These algorithms are implemented in the CLAWPACK software, which is freely available. (C) 2000 Academic Press.