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Computation 2015, 3(4), 670-686; doi:10.3390/computation3040670

Multiscale Simulations for Coupled Flow and Transport Using the Generalized Multiscale Finite Element Method

1
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
2
Center for Numerical Porous Media (NumPor), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
3
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
*
Author to whom correspondence should be addressed.
Academic Editors: Qinjun Kang and Li Chen
Received: 9 October 2015 / Revised: 19 November 2015 / Accepted: 1 December 2015 / Published: 11 December 2015
(This article belongs to the Special Issue Advances in Modeling Flow and Transport in Porous Media)
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Abstract

In this paper, we develop a mass conservative multiscale method for coupled flow and transport in heterogeneous porous media. We consider a coupled system consisting of a convection-dominated transport equation and a flow equation. We construct a coarse grid solver based on the Generalized Multiscale Finite Element Method (GMsFEM) for a coupled system. In particular, multiscale basis functions are constructed based on some snapshot spaces for the pressure and the concentration equations and some local spectral decompositions in the snapshot spaces. The resulting approach uses a few multiscale basis functions in each coarse block (for both the pressure and the concentration) to solve the coupled system. We use the mixed framework, which allows mass conservation. Our main contributions are: (1) the development of a mass conservative GMsFEM for the coupled flow and transport; (2) the development of a robust multiscale method for convection-dominated transport problems by choosing appropriate test and trial spaces within Petrov-Galerkin mixed formulation. We present numerical results and consider several heterogeneous permeability fields. Our numerical results show that with only a few basis functions per coarse block, we can achieve a good approximation. View Full-Text
Keywords: multiscale; mixed; multiscale finite element method; flow; transport multiscale; mixed; multiscale finite element method; flow; transport
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Chung, E.T.; Efendiev, Y.; Leung, W.T.; Ren, J. Multiscale Simulations for Coupled Flow and Transport Using the Generalized Multiscale Finite Element Method. Computation 2015, 3, 670-686.

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