Ecient fully-coupled solution techniques for two-phase ̄ow in porous media Parallel multigrid solution and large scale computations

This paper is concerned with the fast resolution of nonlinear and linear algebraic equations arising from a fully implicit ®nite volume discretization of two-phase ̄ow in porous media. We employ a Newton-multigrid algorithm on unstructured meshes in two and three space dimensions. The discretized operator is used for the coarse grid systems in the multigrid method. Problems with discontinuous coecients are avoided by using a newly truncated restriction operator and an outer Krylov-space method. We show an optimal order of convergence for a wide range of two-phase ̄ow problems including heterogeneous media and vanishing capillary pressure in an experimental way. Furthermore, we present a data parallel implementation of the algorithm with speedup results. Ó 1999 Elsevier Science Ltd. All rights reserved.