An adaptive local–global multiscale finite volume element method for two-phase flow simulations

Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine scale permeability variations through the calculation of specialized coarse scale basis functions. Most of the multiscale techniques presented to date employ localization approximations in the calculation of these basis functions. For some highly correlated (e.g., channelized) formations, however, global effects are important and these may need to be incorporated into the multiscale basis functions. This can be accomplished using global fine scale simulations, but this may be computationally expensive. In this paper an adaptive local–global technique, originally developed within the context of upscaling, is applied for the computation of multiscale basis functions. The procedure enables the efficient incorporation of approximate global information, determined via coarse scale simulations, into the multiscale basis functions. The resulting procedure is formulated as a finite volume element method and is applied for a number of single- and two-phase flow simulations of channelized two-dimensional systems. Both conforming and nonconforming procedures are considered. The level of accuracy of the resulting method is shown to be consistently higher than that of the standard finite volume element multiscale technique based on localized basis functions determined using linear pressure boundary conditions.