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\(\delta\)-mapping algorithm coupled with WENO reconstruction for nonlinear elasticity in heterogeneous media. (English) Zbl 1102.74047
Summary: A newly proposed \(\delta\)-mapping algorithm [P. Zhang and R. X. Liu, J. Comput. Appl. Math. 156, 1–21 (2003); ibid. 176, 105–129 (2005)] is extended to solve compressional elastic wave propagation in nonlinear heterogeneous media, which is characterized by spatially varying flux functions. The algorithm is coupled with the weighted essentially non-oscillatory (WENO) reconstruction, so that the property of high accuracy is preserved. Without the \(\delta\)-mapping procedure, in contrast, the direct application of the WENO scheme is indicated to be deficient.

MSC:
74S10 Finite volume methods applied to problems in solid mechanics
74J30 Nonlinear waves in solid mechanics
74B20 Nonlinear elasticity
Keywords:
waves; layered media
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