Finite element multigrid methods for two-phase immiscible flow in heterogeneous media

Multigrid methods are described for solving the pressure equation arising f rom a finite element discretization of the equations modelling the flow of two immiscible and incompressible fluids in a heterogeneous porous medium. Comparisons are made between the performance of these methods and a precond itioned conjugate gradient algorithm by solving some two-dimensional five s pot problems on both homogeneous and heterogeneous media. Multigrid appears more suitable for large, three-dimensional problems since the number of mu ltigrid cycles required to solve the pressure equation remains constant as the problem size is increased. Copyright (C) 1999 John Wiley & Sons, Ltd.