**Finite Volume Methods for Nonlinear Elasticity
in Heterogeneous Media
**

by R. J. LeVeque,
*Int. J. Numer. Meth. Fluids* 40 (2002), pp. 93-104.

Presented at

ICFD Conference on Numerical Methods for Fluid Dynamics,

Oxford University, March, 2001.

**Abstract.**
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.

Errata: p. 97, equation (11) is missing a minus sign (this wave speed is negative)

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