Expanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Media

Handle URI:
http://hdl.handle.net/10754/598277
Title:
Expanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Media
Authors:
Jiang, L.; Copeland, D.; Moulton, J. D.
Abstract:
We develop a family of expanded mixed multiscale finite element methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed multiscale finite element formulation in the sense that four unknowns (hybrid formulation) are solved simultaneously: pressure, gradient of pressure, velocity, and Lagrange multipliers. We use multiscale basis functions for both the velocity and the gradient of pressure. In the expanded mixed MsFEM framework, we consider both separable and nonseparable spatial scales. Specifically, we analyze the methods in three categories: periodic separable scales, G-convergent separable scales, and a continuum of scales. When there is no scale separation, using some global information can significantly improve the accuracy of the expanded mixed MsFEMs. We present a rigorous convergence analysis of these methods that includes both conforming and nonconforming formulations. Numerical results are presented for various multiscale models of flow in porous media with shale barriers that illustrate the efficacy of the proposed family of expanded mixed MsFEMs. © 2012 Society for Industrial and Applied Mathematics.
Citation:
Jiang L, Copeland D, Moulton JD (2012) Expanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Media. Multiscale Model Simul 10: 418–450. Available: http://dx.doi.org/10.1137/11083143X.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
Multiscale Modeling & Simulation
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Jan-2012
DOI:
10.1137/11083143X
Type:
Article
ISSN:
1540-3459; 1540-3467
Sponsors:
This author's research was supported by the Department of Energy at Los Alamos National Laboratory under contract DE-AC52-06NA25396 and the DOE Office of Science Advanced Computing Research (ASCR) program in Applied Mathematical Sciences.This author's research was supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorJiang, L.en
dc.contributor.authorCopeland, D.en
dc.contributor.authorMoulton, J. D.en
dc.date.accessioned2016-02-25T13:17:51Zen
dc.date.available2016-02-25T13:17:51Zen
dc.date.issued2012-01en
dc.identifier.citationJiang L, Copeland D, Moulton JD (2012) Expanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Media. Multiscale Model Simul 10: 418–450. Available: http://dx.doi.org/10.1137/11083143X.en
dc.identifier.issn1540-3459en
dc.identifier.issn1540-3467en
dc.identifier.doi10.1137/11083143Xen
dc.identifier.urihttp://hdl.handle.net/10754/598277en
dc.description.abstractWe develop a family of expanded mixed multiscale finite element methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed multiscale finite element formulation in the sense that four unknowns (hybrid formulation) are solved simultaneously: pressure, gradient of pressure, velocity, and Lagrange multipliers. We use multiscale basis functions for both the velocity and the gradient of pressure. In the expanded mixed MsFEM framework, we consider both separable and nonseparable spatial scales. Specifically, we analyze the methods in three categories: periodic separable scales, G-convergent separable scales, and a continuum of scales. When there is no scale separation, using some global information can significantly improve the accuracy of the expanded mixed MsFEMs. We present a rigorous convergence analysis of these methods that includes both conforming and nonconforming formulations. Numerical results are presented for various multiscale models of flow in porous media with shale barriers that illustrate the efficacy of the proposed family of expanded mixed MsFEMs. © 2012 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis author's research was supported by the Department of Energy at Los Alamos National Laboratory under contract DE-AC52-06NA25396 and the DOE Office of Science Advanced Computing Research (ASCR) program in Applied Mathematical Sciences.This author's research was supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectExpanded mixed multiscale finite element methodsen
dc.subjectHybridizationen
dc.subjectNonseparable scalesen
dc.subjectTwo-phase flowsen
dc.titleExpanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Mediaen
dc.typeArticleen
dc.identifier.journalMultiscale Modeling & Simulationen
dc.contributor.institutionLos Alamos National Laboratory, Los Alamos, United Statesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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