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

Published online by Cambridge University Press:  20 August 2015

Lijian Jiang  and
Ilya D. Mishev
Lijian Jiang*
Affiliation:
Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 55455, USA
Ilya D. Mishev*
Affiliation:
ExxonMobil Upstream Research Company, Houston, TX 77252, USA
*
Corresponding author.Email:lijiang@ima.umn.edu
Email:ilya.d.mishev@exxonmobil.com
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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 [20]; 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.

Keywords

65N3065N2034E13Mixed multiscale finite volume methodselliptic equationstwo-phase flowsheterogeneous porous media
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 1 , January 2012 , pp. 19 - 47
Copyright
Copyright © Global Science Press Limited 2012

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