Implicit scheme and domain decomposition method for multiphase fluid flow in porous medium

We are concerned with incompressible three-phase fluid flow in sedimentary basins cut by faults along which block displacements can occur (CERES project). In order to handle these complex geometries, we use Domain Decomposition (DD) techniques. Indeed, faults divide the basin into blocks that naturally define computational subdomains. The mathematical model that describes the physical phenomena leads to a strongly coupled nonlinear system of a hyperbolic equation for saturation and a parabolic equation for pressure.