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 sc heme for the accurate solution of elliptic diffusion equations with st rongly 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, wh ich may occur if the medium is anisotropic in a general direction. Suc h problems arise, for example, in oil reservoir simulation, when renor malisation techniques are used to model the reservoir geology. It is i n 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 mu ltigrid scheme for efficient numerical solution of the algebraic equat ions derived using the new discretisation. (C) 1995 Academic Press, In c.