Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method

JOURNAL OF COMPUTATIONAL PHYSICS

卷:299

Article

Petersson, N. Anders¹  Sjoegreen, Bjoern¹ 

[1] Lawrence Livermore Natl Lab, Ctr Appl Sci Comp, Livermore, CA 94551 USA

关键词: Anisotropy;    Elastic wave equation;    Curvilinear coordinates;    Far-field closure;    Summation-by-parts;   

DOI  :  10.1016/j.jcp.2015.07.023

来源: Elsevier

【 摘 要 】

We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjogreen and Petersson (2012) [11]. The proposed method discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. We also generalize and evaluate the super-grid far-field technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. As a result, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals. Published by Elsevier Inc.

【 授权许可】

Free