Numerical modelling of void inclusions in porous media

Numerical modelling of porous flow in a low-permeability matrix with high-permeability inclusions is a challenging task because the large ratio of permeabilities ill-conditions the finite element system of equations. We propose a coupled model where Darcy flow is used for the porous matrix and potential flow is used for the inclusions. We discuss appropriate interface conditions in detail and show that the head drop in the inclusions can be prescribed in a very simple way. Algorithmic aspects are treated in full detail. Numerical examples show that this coupled approach precludes ill-conditioning and is more efficient than heterogeneous Darcy flow