Mixed Multiscale Finite Volume Methods for Elliptic Problems in Two-phase Flow Simulations

TL;DR

This paper introduces a flexible framework for mixed multiscale finite volume methods tailored for elliptic equations in porous media, enhancing accuracy and efficiency in two-phase flow simulations with complex multiscale features.

Contribution

It presents new and existing mixed MsFV methods, including novel multiscale velocity basis functions that incorporate global information for improved accuracy.

Findings

Accurately captures small-scale effects on coarse grids

Demonstrates efficiency in heterogeneous porous media simulations

Validates methods with numerical examples showing high accuracy

Abstract

We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known \cite{jennylt03}; others are new. New insight is gained for the known methods and extra flexibility is provided by the new methods. We give as an example a mixed MsFV on uniform mesh in 2-D. This method uses novel multiscale velocity basis functions that are suited for using global information, which is often needed to improve the accuracy of the multiscale 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 new mixed MsFV and apply it to solve two-phase flow equations in heterogeneous porous media. Numerical examples demonstrate the accuracy and efficiency of the proposed method for modeling the flows in porous media with non-separable and separable scales.