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)

Preprint: .ps.gz

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