Two phase flow conclusion
We succeeded to implement the solver and resolve problems such as the problem of negative saturation.
However some cases with high rate flow production are not yet stabilize and leads to a saturation superior to one which causes a divergence of the solver.
The study of viscous flow and in domains with small permeability has shown that we have a limit on the rate flow of production. Indeed when this limit is reached a "hole" is created in the liquid saturation field.