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Finite‐volume methods for non‐linear elasticity in heterogeneous media
Author(s) -
LeVeque Randall J.
Publication year - 2002
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.309
Subject(s) - riemann solver , solver , riemann problem , mathematical analysis , elasticity (physics) , mathematics , linear elasticity , finite volume method , riemann hypothesis , physics , mechanics , finite element method , mathematical optimization , thermodynamics
An approximate Riemann solver is developed for the equations of non‐linear elasticity in a heterogeneous medium, where each grid cell has an associated density and stress–strain relation. The non‐linear 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 non‐linearity, lead to solitary wave solutions that are well captured by the numerical method. Copyright © 2002 John Wiley & Sons, Ltd.