DISCRETIZATION AND MULTIGRID SOLUTION OF ELLIPTIC-EQUATIONS WITH MIXED DERIVATIVE TERMS AND STRONGLY DISCONTINUOUS COEFFICIENTS

This paper introduces a new conservative cell centred finite volume scheme for the accurate solution of elliptic diffusion equations with strongly varying coefficients. The discretisation is designed to model a wide range of heterogeneities and anisotropies, and in particular the case where the diffusivity is represented by a nondiagonal matrix, which may occur if the medium is anisotropic in a general direction. Such problems arise, for example, in oil reservoir simulation, when renormalisation techniques are used to model the reservoir geology. It is in this context that the method is described, although it is applicable to a far wider class of problems in heat conduction, electrostatics, and potential theory. The paper also describes the application of a multigrid scheme for efficient numerical solution of the algebraic equations derived using the new discretisation. (C) 1995 Academic Press, Inc.