Wave Propagation Algorithms for Multidimensional Hyperbolic Systems

In one space dimension the standard conservation law has the form 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 qt 1 f(q)x 5 0, (1) applying limiter functions to the resulting waves, which are then propagated in a multidimensional manner. For nonlinear systems where q [ R is the vector of conserved quantities. Here of conservation laws the methods are conservative and yield good shock resolution. The methods are generalized to hyperbolic syswe also consider the more general variable-coefficient quatems that are not in conservation form and to problems that include silinear form a ‘‘capacity function.’’ Several examples are included for gas dynamics, acoustics in a heterogeneous medium, and advection in a straqt 1 A(q, x, t)qx 5 0, (2) tified flow on curvilinear grids. The software package CLAWPACK implements these algorithms in Fortran and is freely available on the Web. One and two space dimensions are discussed here, although and the methods are formulated in a general manner that the algorithms and software have also been extended to three also allows their application to hyperbolic systems that dimensions. Q 1997 Academic Press are not in conservation form, e.g., the variable-coefficient linear systems of equations for acoustic or elastic wave propagation in a heterogeneous medium.