Mode decomposition methods for flows in high-contrast porous media. Global-local approach

Handle URI:
http://hdl.handle.net/10754/563058
Title:
Mode decomposition methods for flows in high-contrast porous media. Global-local approach
Authors:
Ghommem, Mehdi; Presho, Michael; Calo, Victor M. ( 0000-0002-1805-4045 ) ; Efendiev, Yalchin R. ( 0000-0001-9626-303X )
Abstract:
In this paper, we combine concepts of the generalized multiscale finite element method (GMsFEM) and mode decomposition methods to construct a robust global-local approach for model reduction of flows in high-contrast porous media. This is achieved by implementing Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) techniques on a coarse grid computed using GMsFEM. The resulting reduced-order approach enables a significant reduction in the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider a variety of high-contrast coefficients and present the corresponding numerical results to illustrate the effectiveness of the proposed technique. This paper is a continuation of our work presented in Ghommem et al. (2013) [1] where we examine the applicability of POD and DMD to derive simplified and reliable representations of flows in high-contrast porous media on fully resolved models. In the current paper, we discuss how these global model reduction approaches can be combined with local techniques to speed-up the simulations. The speed-up is due to inexpensive, while sufficiently accurate, computations of global snapshots. © 2013 Elsevier Inc.
KAUST Department:
Numerical Porous Media SRI Center (NumPor); Applied Mathematics and Computational Science Program; Earth Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
Nov-2013
DOI:
10.1016/j.jcp.2013.06.033
ARXIV:
arXiv:1301.5742
Type:
Article
ISSN:
00219991
Sponsors:
YE's work is partially supported by the US DoD, DOE and NSF (DMS 0934837, DMS 0724704, and DMS 0811180).
Additional Links:
http://arxiv.org/abs/arXiv:1301.5742v1
Appears in Collections:
Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGhommem, Mehdien
dc.contributor.authorPresho, Michaelen
dc.contributor.authorCalo, Victor M.en
dc.contributor.authorEfendiev, Yalchin R.en
dc.date.accessioned2015-08-03T11:34:49Zen
dc.date.available2015-08-03T11:34:49Zen
dc.date.issued2013-11en
dc.identifier.issn00219991en
dc.identifier.doi10.1016/j.jcp.2013.06.033en
dc.identifier.urihttp://hdl.handle.net/10754/563058en
dc.description.abstractIn this paper, we combine concepts of the generalized multiscale finite element method (GMsFEM) and mode decomposition methods to construct a robust global-local approach for model reduction of flows in high-contrast porous media. This is achieved by implementing Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) techniques on a coarse grid computed using GMsFEM. The resulting reduced-order approach enables a significant reduction in the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider a variety of high-contrast coefficients and present the corresponding numerical results to illustrate the effectiveness of the proposed technique. This paper is a continuation of our work presented in Ghommem et al. (2013) [1] where we examine the applicability of POD and DMD to derive simplified and reliable representations of flows in high-contrast porous media on fully resolved models. In the current paper, we discuss how these global model reduction approaches can be combined with local techniques to speed-up the simulations. The speed-up is due to inexpensive, while sufficiently accurate, computations of global snapshots. © 2013 Elsevier Inc.en
dc.description.sponsorshipYE's work is partially supported by the US DoD, DOE and NSF (DMS 0934837, DMS 0724704, and DMS 0811180).en
dc.publisherElsevier BVen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1301.5742v1en
dc.subjectDynamic mode decompositionen
dc.subjectGeneralized multiscale finite element methoden
dc.subjectHeterogeneous porous mediaen
dc.subjectModel reductionen
dc.subjectProper orthogonal decompositionen
dc.titleMode decomposition methods for flows in high-contrast porous media. Global-local approachen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentEarth Science and Engineering Programen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionDepartment of Mathematics And Institute for Scientific Computation (ISC), Texas A And M University, College Station, TX, United Statesen
dc.identifier.arxividarXiv:1301.5742en
kaust.authorGhommem, Mehdien
kaust.authorCalo, Victor M.en
kaust.authorEfendiev, Yalchin R.en
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