An Efficient Meshless Method for Simulating Wave Motions in Saturated Porous Media

Abstract

An efficient meshless local Petrov-Galerkin (MLPG) method is proposed and applied to simulate the wave motions in saturated porous media. Firstly, A weak formulation for the governing equations in Biot’s theory is obtained by local Petrov-Galerkin method. The meshless approximation based on the Radial Point Interpolation Method (RPIM) is employed for the implementation. Then, The lumped mass is employed considering the accuracy of wave simulation, and the time intergration is performed in an explicit way. Due to the Kronecker Delta properties of the shape function derived by RPIM, no additional treatment is needed to impose the essential boundary condition. Thus, an explicit decoupled meshless method is derived, it avoids solving large system of linear equations on each time step. At last, a two-dimensional problem is studied and compared with finite element method solution.