A meshless singular boundary method for elastic wave propagation in 2D partially saturated poroelastic media

Abstract

This paper presents a boundary meshless method, singular boundary method (SBM), in conjunction with the exponential window method (EWM) to simulate the dynamic response of the 2D partially saturated poroelastic media. The problem is firstly solved in the frequency-domain resulted from the time-domain governing equations via the Fourier transformation. Then the SBM approximates the solutions with a linear combination of fundamental solutions with respect to the source points on the physical boundary. To successfully apply the SBM, two issues are addressed. Firstly, the kernel functions, namely the fundamental solutions of frequency-domain governing equations, are derived based on the eigen-analysis. Secondly, the source singularities of the fundamental solutions are desingularized with analytical formulas. After obtaining the SBM formulation, the time-domain solutions can be obtained by the EWM, where the frequency domain windowing technique is introduced to stabilize the oscillations caused by damping parameters. Four numerical examples are carried out to show the validity and accuracy of the proposed method.