A numerical method based on finite difference approximations is presented for the calculation of the time dependent deformation, pressure and flow within a finite two-dimensional poroelastic medium. The method allows for sources or sinks of fluid within the medium, slip or no slip boundaries, a permeable or impermeable free surface and applied pressures or forces at the boundaries. The applications of this method are varied and include filtration problems, soil consolidation, and the indentation of biological tissue.
Mercer, G. N., & Barry, S. I. (1999). Flow and deformation in poroelasticity - II: Numerical method. Mathematical and Computer Modelling, 30(9–10), 31–38. https://doi.org/10.1016/S0895-7177(99)00178-8