Elimination of adaptive grid interface errors in the discrete cell centered pressure equation

Classical cell centered discretization of the reservoir simulation pressure equation on an h-adaptive grid results in an O(1/h) leading truncation error at the grid interface. A new flux continuous finite volume correction is presented together with an improved version of a previously proposed correction. While both corrections eliminate the leading error, the new correction exhibits the best convergence rates and has the following properties: the resulting matrix is in general symmetric positive definite, diagonally dominant for locally isotropic spatially varying coefficients, convergence to O(h) is demonstrated, and support of the standard approximation is retained, ensuring a fully implicit implementation. Results computed by the uncorrected classical scheme and both correction schemes are compared for two phase flow simulations with multilevel dynamic local grid refinement. (C) 1996 Academic Press, Inc.