This is an example of heterogeneous benchmark problem for incompressible two-phase flow in porous media.
The problem is solved with high order, implicit, fully coupled Discontinuous Galerkin Methods. The injection well is located at the bottom left corner of the domain (water enters through the injection well) and the production well is located at the top right corner (oil is pushed out from this well).

Numerical solution is obtained on coarse unstructured triangular mesh (66 els) with discontinuous polynomial approximation of order 4 for pressure, and of order 2 for saturation. The movie shows how water fills out the domain, trying to avoid lower permeability zone. The color represents the saturation of water in porous media.