Finite Volume Methods for Nonlinear Elasticity in Heterogeneous Media

An approximate Riemann solver is developed for the equations of nonlinear elasticity in a heterogeneous medium, where each grid cell has an associated density and stress-strain relation. The nonlinear flux function is spatially varying and a wave decomposition of the flux difference across a cell interface is used to approximate the wave structure of the Riemann solution. This solver is used in conjunction with a high-resolution finite-volume method using the CLAWPACK software. As a test problem, elastic waves in a periodic layered medium are studied. Dispersive effects from the heterogeneity, combined with the nonlinearity, lead to solitary wave solutions that are well captured by the numerical method.