Mixed Multiscale Finite Volume Methods for Elliptic Problems in Two-Phase Flow Simulations (Communications in Computational Physics, 2012)
We develop a framework for constructing mixed multiscale finite volumemethods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known [20];others are new. New insight is gained for the known methods and extra flexibilityis provided by the new methods. We give as an example a mixed MsFV on uniformmesh in 2-D. This method uses novel multiscale velocity basis functions that are suitedfor using global information, which is often needed to improve the accuracy of themultiscale simulations in the case of continuum scales with strong non-local features.The method efficiently captures the small effects on a coarse grid. We analyze the newmixed MsFV and apply it to solve two-phase flow equations in heterogeneous porousmedia. Numerical examples demonstrate the accuracy and efficiency of the proposedmethod for modeling the flows in porous media with non-separable and separablescales.