Online Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Media

Handle URI:
http://hdl.handle.net/10754/618025
Title:
Online Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Media
Authors:
Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Gildin, Eduardo; Yang, Yanfang ( 0000-0002-8385-8306 )
Abstract:
We propose an online adaptive local-global POD-DEIM model reduction method for flows in heterogeneous porous media. The main idea of the proposed method is to use local online indicators to decide on the global update, which is performed via reduced cost local multiscale basis functions. This unique local-global online combination allows (1) developing local indicators that are used for both local and global updates (2) computing global online modes via local multiscale basis functions. The multiscale basis functions consist of offline and some online local basis functions. The approach used for constructing a global reduced system is based on Proper Orthogonal Decomposition (POD) Galerkin projection. The nonlinearities are approximated by the Discrete Empirical Interpolation Method (DEIM). The online adaption is performed by incorporating new data, which become available at the online stage. Once the criterion for updates is satisfied, we adapt the reduced system online by changing the POD subspace and the DEIM approximation of the nonlinear functions. The main contribution of the paper is that the criterion for adaption and the construction of the global online modes are based on local error indicators and local multiscale basis function which can be cheaply computed. Since the adaption is performed infrequently, the new methodology does not add significant computational overhead associated with when and how to adapt the reduced basis. Our approach is particularly useful for situations where it is desired to solve the reduced system for inputs or controls that result in a solution outside the span of the snapshots generated in the offline stage. Our method also offers an alternative of constructing a robust reduced system even if a potential initial poor choice of snapshots is used. Applications to single-phase and two-phase flow problems demonstrate the efficiency of our method.
KAUST Department:
Numerical Porous Media SRI Center (NumPor)
Citation:
Online Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Media 2016, 4 (2):22 Computation
Publisher:
MDPI AG
Journal:
Computation
Issue Date:
7-Jun-2016
DOI:
10.3390/computation4020022
Type:
Article
ISSN:
2079-3197
Sponsors:
This publication also was made possible by a National Priorities Research Program grant NPRP grant 7-1482-1278 from the Qatar National Research Fund (a member of The Qatar Foundation). Y.E. and E.G. would like to thank the partial support from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-FG02-13ER26165 and the DoD Army ARO Project.
Additional Links:
http://www.mdpi.com/2079-3197/4/2/22
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorGildin, Eduardoen
dc.contributor.authorYang, Yanfangen
dc.date.accessioned2016-08-08T10:49:01Z-
dc.date.available2016-08-08T10:49:01Z-
dc.date.issued2016-06-07-
dc.identifier.citationOnline Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Media 2016, 4 (2):22 Computationen
dc.identifier.issn2079-3197-
dc.identifier.doi10.3390/computation4020022-
dc.identifier.urihttp://hdl.handle.net/10754/618025-
dc.description.abstractWe propose an online adaptive local-global POD-DEIM model reduction method for flows in heterogeneous porous media. The main idea of the proposed method is to use local online indicators to decide on the global update, which is performed via reduced cost local multiscale basis functions. This unique local-global online combination allows (1) developing local indicators that are used for both local and global updates (2) computing global online modes via local multiscale basis functions. The multiscale basis functions consist of offline and some online local basis functions. The approach used for constructing a global reduced system is based on Proper Orthogonal Decomposition (POD) Galerkin projection. The nonlinearities are approximated by the Discrete Empirical Interpolation Method (DEIM). The online adaption is performed by incorporating new data, which become available at the online stage. Once the criterion for updates is satisfied, we adapt the reduced system online by changing the POD subspace and the DEIM approximation of the nonlinear functions. The main contribution of the paper is that the criterion for adaption and the construction of the global online modes are based on local error indicators and local multiscale basis function which can be cheaply computed. Since the adaption is performed infrequently, the new methodology does not add significant computational overhead associated with when and how to adapt the reduced basis. Our approach is particularly useful for situations where it is desired to solve the reduced system for inputs or controls that result in a solution outside the span of the snapshots generated in the offline stage. Our method also offers an alternative of constructing a robust reduced system even if a potential initial poor choice of snapshots is used. Applications to single-phase and two-phase flow problems demonstrate the efficiency of our method.en
dc.description.sponsorshipThis publication also was made possible by a National Priorities Research Program grant NPRP grant 7-1482-1278 from the Qatar National Research Fund (a member of The Qatar Foundation). Y.E. and E.G. would like to thank the partial support from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-FG02-13ER26165 and the DoD Army ARO Project.en
dc.language.isoenen
dc.publisherMDPI AGen
dc.relation.urlhttp://www.mdpi.com/2079-3197/4/2/22en
dc.rightsArchived with thanks to Computation. This is an open access article distributed under the Creative Commons Attribution License (CC BY 4.0). https://creativecommons.org/licenses/by-nc-sa/4.0/en
dc.subjectonline adaptive model reductionen
dc.subjectlocal model reductionen
dc.subjectPOD global model reductionen
dc.subjectdiscrete empirical interpolation methoden
dc.subjectflows in heterogeneous mediaen
dc.titleOnline Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Mediaen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalComputationen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Mathematics, Texas A&M University, College Station, TX 77843, USAen
dc.contributor.institutionDepartment of Petroleum Engineering, Texas A&M University, College Station, TX 77843, USAen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorEfendiev, Yalchin R.en
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