Wave Propagation Methods for Conservation Laws with Source Terms

Abstract

An inhomogeneous system of conservation laws will exhibit steady solutions when flux gradients are balanced by source terms. These steady solutions are difficult for many numerical methods (e.g., fractional step methods) to capture and maintain. Recently, a quasi-steady wave-propagationalgorithm was developed and used to compute near-steady shallow water flow over variable topography. In this paper we extend this algorithm to near-steady flow of an ideal gas subject to a static gravitational field. The method is implemented in the software package CLAWPACK. The ability of this method to capture perturbed quasi-steady solutions is demonstrated with numerical examples.