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

Abstract

Multigrid methods are described for solving the pressure equation arising from 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 preconditioned conjugate gradient algorithm by solving some two-dimensional five spot problems on both homogeneous and heterogeneous media. Multigrid appears more suitable for large, three-dimensional problems since the number of multigrid cycles required to solve the pressure equation remains constant as the problem size is increased