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Wave Propagation Algorithms for Multidimensional Hyperbolic Systems

A class of high resolution multidimensional wave-propagation algorithms is described for general time-dependent hyperbolic systems. The methods are based on solving Riemann problems and applying limiter functions to the resulting waves, which are then propagated in a multidimensional manner. For nonlinear systems of conservation laws the methods are conservative and yield good shock resolution. The methods are generalized to hyperbolic systems that are not in conservation form and to problems that include a “capacity function.” Several examples are included for gas dynamics, acoustics in a heterogeneous medium, and advection in a stratified flow on curvilinear grids. The software packageCLAWPACKimplements these algorithms in Fortran and is freely available on the Web. One and two space dimensions are discussed here, although the algorithms and software have also been extended to three dimensions.