A completely explicit finite element method for solving dynamic u-p equations of fluid-saturated porous media

A completely explicit finite element method is developed to efficiently solve the dynamic u-p equations of fluid-saturated porous media (FSPM). In the spatial domain, a diagonalization method is applied to both the mass and the fluid compressibility matrices by neglecting the interactions between adjacent nodes in the finite element model of FSPM for the first time. In the time domain, an explicit-explicit algorithm consisting of the central and the unilateral difference methods is applied to solve the dynamic u-p equations. The stability and accuracy of the proposed explicit-explicit algorithm are discussed. Moreover, five numerical examples were presented in this paper. The good agreements between the results obtained from the proposed method and the existing explicit-implicit method indicate that the diagonalization method for the fluid compressibility matrix and the proposed completely explicit method are validity in solving the dynamic u-p equations of FSPM.