Assessment of finite difference methods to solve porous media dynamics

A number of methods have been developed for solving the dynamics of saturated porous media, mostly based on the finite element method. However, few works have discussed how to solve dynamic problems with the Finite Difference Method (FDM). The FDM cannot easily fulfil the Ladyzenskaja- Babuska-Brezzi (LBB) stability criteria because it uses same order spatial discretisations. Nonetheless, some stabilization techniques were introduced in the literature. This paper aims to explore the possibilities of solutions with the FDM, including an assessment of accuracy, efficiency and stability of proposed methods. In this contribution, some FDM schemes are developed and a comparative study is presented. Simulations of a 1D and 2D wave propagation problems are performed in order to reveal the advantages and drawbacks of all schemes