High-resolution finite-volume methods for acoustic waves in periodic and random media

High-resolution numerical methods originally developed for shock capturing in the context of nonlinear conservation laws are found to be very useful for solving acoustics problems in rapidly varying heterogeneous media. These methods are based on solving Riemann problems at the interface between grid cells, which resolve waves into transmitted and reflected components at each interface. The wave-propagation method developed in R. J. LeVeque [J. Comput. Phys. 131, 327 endash 353 (1997)] and implemented in the CLAWPACK software package is tested on several acoustics problems with periodic or random media in one and two space dimensions. A new limiter function is presented for solving problems in a periodic medium where numerical instabilities are observed with standard limiters. copyright 1999 Acoustical Society of America.