Multigrid Methods for Three-Dimensional Petroleum Reservoir Simulation

Abstract

ABSTRACT The purpose of this paper is to report on a preliminary study of a new multigrid scheme for solving three-dimensional problems of the type that arise from pressure equations in reservoir simulation. The basic idea of this new approach is to use both semi-coarsening and plane relaxation in order to accommodate all types of anisotropies and heterogeneities. The scheme also simplifies and reduces the cost of the setup involved in automatic coarsening of the fine-grid equations. This paper presents the results of the new approach applied to several known test problems. A comparison of performance and complexity is made with the best solvers now in widespread use in reservoir simulation.