Numerical Solution of Biot Equations in Quasi-static State

Abstract

This paper presents a numerical algorithm to simulate low-frequency loading of fluid-filled poroelastic materials and estimate the effective frequency-dependent strain-stress relations for such media. The algorithm solves Biot equation in quasi-static state in the frequency domain. Thus, a large-scale system of linear algebraic equations have to be solved for each temporal frequency. We use the direct solver, based on the LU decomposition to resolve the system of the linear equations. According to the presented numerical examples suggested algorithm allows reconstructing the stiffness tensor within a wide range of frequencies for the realistic large-scale samples within several minutes. Thus, the estimation of the frequency-dependent stiffness tensors can be done in a routine manner and statistical data may be accumulated.