Numerical Simulation of Biot-wave equation in porous medium

Xinming Zhang Chaoying Zhou Jiaqi Liu Ke’an Liu 1 Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China 2 Professor, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China 3, 4 Professor, Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China Email: [email protected],[email protected] ABSTRACT: In this paper, a wavelet Galerkin finite element method is proposed by combing the wavelet analysis with traditional finite element method to analyze wave propagation phenomena in fluid-saturated porous medium. The scaling functions of Daubechies wavelets are considered as the interpolation basis functions to replace the polynomial functions, and then the wavelet element is constructed. In order to overcome the integral difficulty for lacking of the explicit expression for the Daubechies wavelets, a kind of characteristic function are introduced. The recursive expression of calculating the function value of Daubechies wavelets on the fraction nodes is deduced, and the rapid wavelet transform between the wavelet coefficient space and the wave field displacement space is constructed. The results of numerical simulation demonstrate the method is effective.