Communications in Mathematical Sciences

Volume 12 (2014)

Number 1

Exact nonreflecting boundary conditions for three dimensional poroelastic wave equations

Pages: 61 – 98

DOI: https://dx.doi.org/10.4310/CMS.2014.v12.n1.a4

Authors

Wensheng Zhang (LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China)

Li Tong (LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China)

Eric T. Chung (Department of Mathematics, The Chinese University of Hong Kong)

Abstract

Simulation of waves in complex poroelastic media is crucial in providing important geophysical information that cannot be obtained via simple elastic or acoustic models. Thus there is a need to design an artificial boundary condition for simulation using the numerical approximation of such a problem. In this paper, our aim is to derive an exact nonreflecting boundary condition for the three dimensional poroelastic wave equations based on the Grote-Keller method. The proposed boundary condition is nonlocal in space, but local in time and can be coupled easily with standard numerical approaches for the computation of numerical solutions. Numerical results computed by the finite difference method demonstrate the effectiveness of our method.

Keywords

poroelastic wave equations, wave propagation in porous media, exact nonreflecting boundary conditions, artificial boundary conditions

2010 Mathematics Subject Classification

35L05, 35L20, 35Mxx, 78A40, 78A45

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Published 20 August 2013