Adaptive multiscale methods for multiphase simulation of complex reservoir models

Many multiscale methods for solving elliptic/parabolic flow equations can be written in operator form using a restriction and a prolongation operator defined over a coarse partition of an underlying fine grid. The restriction operator constructs a reduced system of flow equations on the coarse partition and the prolongation operator maps pressure unknowns from the coarse partition onto the original simulation grid. In the talk, we demonstrate that applying a sequence of such operator pairs that adapt to geological structures, well paths, and dynamic changes in primary variables gives significantly faster convergence than applying a single operator pair associated with a fixed partition.