Efficient algorithms for multiscale modeling in porous media

Handle URI:
http://hdl.handle.net/10754/598097
Title:
Efficient algorithms for multiscale modeling in porous media
Authors:
Wheeler, Mary F.; Wildey, Tim; Xue, Guangri
Abstract:
We describe multiscale mortar mixed finite element discretizations for second-order elliptic and nonlinear parabolic equations modeling Darcy flow in porous media. The continuity of flux is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. We discuss the construction of multiscale mortar basis and extend this concept to nonlinear interface operators. We present a multiscale preconditioning strategy to minimize the computational cost associated with construction of the multiscale mortar basis. We also discuss the use of appropriate quadrature rules and approximation spaces to reduce the saddle point system to a cell-centered pressure scheme. In particular, we focus on multiscale mortar multipoint flux approximation method for general hexahedral grids and full tensor permeabilities. Numerical results are presented to verify the accuracy and efficiency of these approaches. © 2010 John Wiley & Sons, Ltd.
Citation:
Wheeler MF, Wildey T, Xue G (2010) Efficient algorithms for multiscale modeling in porous media. Numerical Linear Algebra with Applications 17: 771–785. Available: http://dx.doi.org/10.1002/nla.742.
Publisher:
Wiley-Blackwell
Journal:
Numerical Linear Algebra with Applications
KAUST Grant Number:
(KAUST)-AEA-UTA08-687; KUS-F1-032-04
Issue Date:
26-Sep-2010
DOI:
10.1002/nla.742
Type:
Article
ISSN:
1070-5325
Sponsors:
Contract/grant sponsor: Publishing Arts Research Council; contract grant/number: 98-1846389Contract/grant sponsor: DOE Energy Frontier Research Center; contract/grant number: DE-SC0001114Contract/grant sponsor: NSF-CDI; contract/grant number: DMS 0835745Contract/grant sponsor: King Abdullah University of Science and Technology; contract/grant number: (KAUST)-AEA-UTA08-687Contract/grant sponsor: KAUST; contract/grant number: KUS-F1-032-04
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorWheeler, Mary F.en
dc.contributor.authorWildey, Timen
dc.contributor.authorXue, Guangrien
dc.date.accessioned2016-02-25T13:12:37Zen
dc.date.available2016-02-25T13:12:37Zen
dc.date.issued2010-09-26en
dc.identifier.citationWheeler MF, Wildey T, Xue G (2010) Efficient algorithms for multiscale modeling in porous media. Numerical Linear Algebra with Applications 17: 771–785. Available: http://dx.doi.org/10.1002/nla.742.en
dc.identifier.issn1070-5325en
dc.identifier.doi10.1002/nla.742en
dc.identifier.urihttp://hdl.handle.net/10754/598097en
dc.description.abstractWe describe multiscale mortar mixed finite element discretizations for second-order elliptic and nonlinear parabolic equations modeling Darcy flow in porous media. The continuity of flux is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. We discuss the construction of multiscale mortar basis and extend this concept to nonlinear interface operators. We present a multiscale preconditioning strategy to minimize the computational cost associated with construction of the multiscale mortar basis. We also discuss the use of appropriate quadrature rules and approximation spaces to reduce the saddle point system to a cell-centered pressure scheme. In particular, we focus on multiscale mortar multipoint flux approximation method for general hexahedral grids and full tensor permeabilities. Numerical results are presented to verify the accuracy and efficiency of these approaches. © 2010 John Wiley & Sons, Ltd.en
dc.description.sponsorshipContract/grant sponsor: Publishing Arts Research Council; contract grant/number: 98-1846389Contract/grant sponsor: DOE Energy Frontier Research Center; contract/grant number: DE-SC0001114Contract/grant sponsor: NSF-CDI; contract/grant number: DMS 0835745Contract/grant sponsor: King Abdullah University of Science and Technology; contract/grant number: (KAUST)-AEA-UTA08-687Contract/grant sponsor: KAUST; contract/grant number: KUS-F1-032-04en
dc.publisherWiley-Blackwellen
dc.subjectDomain decompositionen
dc.subjectMortar finite elementen
dc.subjectMultipoint flux approximationen
dc.subjectMultiscaleen
dc.subjectSingle phase flowen
dc.titleEfficient algorithms for multiscale modeling in porous mediaen
dc.typeArticleen
dc.identifier.journalNumerical Linear Algebra with Applicationsen
dc.contributor.institutionUniversity of Texas at Austin, Austin, United Statesen
kaust.grant.number(KAUST)-AEA-UTA08-687en
kaust.grant.numberKUS-F1-032-04en
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