Staggered finite-element solution for water and gas flow in deforming porous media

A numerical model for the mechanics of partially saturated porous media is presented where the flow of both fluid phases is taken into account. The attention is focused on the choice of the field variables so that the model may easily be extended to deal with the important case when the gaseous phase is at constant reference pressure and with the limiting case of a fully saturated situation. To solve the semi-discretized governing differential equation system in the time domain a staggered procedure is presented, which also allows for a straightforward solution of the two aforementioned cases. The stability and convergence analyses of the proposed solution scheme are presented for a 3 degree-of-freedom model system. In this way it is possible to assess the behaviour of the proposed solution scheme.