LeVeque, Randall J. Finite volume methods for nonlinear elasticity in heterogeneous media. (English) Zbl 1024.74044 Int. J. Numer. Methods Fluids 40, No. 1-2, 93-104 (2002). Summary: We develop an approximate Riemann solver for 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 flux difference across the 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, we study elastic waves in a periodic layered medium. Dispersive effects from the heterogeneity, combined with the nonlinearity, lead to solitary wave solutions that are well captured by the present numerical method. Cited in 12 Documents MSC: 74S10 Finite volume methods applied to problems in solid mechanics 74J30 Nonlinear waves in solid mechanics 74B20 Nonlinear elasticity 74E05 Inhomogeneity in solid mechanics Keywords:approximate Riemann solver; nonlinear elasticity; heterogeneous medium; nonlinear flux function; wave decomposition; flux difference; finite volume method; CLAWPACK software; elastic waves; periodic layered medium; solitary wave Software:CLAWPACK PDFBibTeX XMLCite \textit{R. J. LeVeque}, Int. J. Numer. Methods Fluids 40, No. 1--2, 93--104 (2002; Zbl 1024.74044) Full Text: DOI References: [1] LeVeque, Journal of Computational Physics 131 pp 327– (1997) [2] CLAWPACK software. http: //www.amath.washington.edu/?claw [3] High-resolution finite volume methods for acoustics in a rapidly-varying heterogeneous medium. In Mathematical and Numerical Aspects of Wave Propagation, (ed.), Proceedings of the Fourth International Conference on Wave Propagation, Golden, CO, SIAM: Philadelphia, PA, 1998; 603-605. · Zbl 0973.76578 [4] Fogarty, Journal of Acoustical Society of America 106 pp 17– (1999) [5] A wave-propagation method for conservation laws and balance laws with spatially varying flux functions. 2002, submitted (ftp: //amath.washington.edu/pub/rjl/ papers/vcflux.ps.gz) · Zbl 1034.65068 [6] Wave propagation algorithms for hyperbolic systems on curved manifolds. 2002, in preparation. [7] Numerical tests of evolution systems, gauge conditions and boundary conditions for 1d colliding gravitational plane waves. 2002, submitted. [8] LeVeque, Journal of Computational Physics 172 pp 572– (2001) [9] Santosa, SIAM Journal of Applied Mathematics 51 pp 984– (1991) [10] Lax, Communications on Pure and Applied Mathematics 36 pp 809– (1983) [11] Jin, Communications on Pure and Applied Mathematics 48 pp 235– (1995) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.