Nearwell local space and time refinement in reservoir simulation

In reservoir simulations, nearwell regions usually require finer space and time scales compared with the remaining of the reservoir domain. We present a domain decomposition algorithm for a two phase Darcy flow model coupling nearwell regions locally refined in space and time with a coarser reservoir discretization. The algorithm is based on an optimized Schwarz method using a full overlap at the coarse level. The main advantage of this approach is to apply to fully implicit discretizations of general multiphase flow models and to allow a simple optimization of the interface conditions based on a single phase flow equation.