Global-local nonlinear model reduction for flows in heterogeneous porous media

Handle URI:
http://hdl.handle.net/10754/565981
Title:
Global-local nonlinear model reduction for flows in heterogeneous porous media
Authors:
AlOtaibi, Manal; Calo, Victor M. ( 0000-0002-1805-4045 ) ; Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Galvis, Juan; Ghommem, Mehdi
Abstract:
In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual and the Jacobian on a fine grid. As such, we use local and global empirical interpolation concepts to circumvent performing these computations on the fine grid. The resulting reduced-order approach significantly reduces the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider several numerical examples of nonlinear multiscale partial differential equations that are numerically integrated using fully-implicit time marching schemes to demonstrate the capability of the proposed model reduction approach to speed up simulations of nonlinear flows in high-contrast porous media.
KAUST Department:
Numerical Porous Media SRI Center (NumPor); Applied Mathematics and Computational Science Program; Earth Science and Engineering Program
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
Issue Date:
Aug-2015
DOI:
10.1016/j.cma.2014.10.034
ARXIV:
arXiv:1407.0782v1
Type:
Article
ISSN:
00457825
Sponsors:
YE's work is partially supported by the US 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, and the grant FA9550-11-1-0341 from the Air Force Office of Scientific Research.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorAlOtaibi, Manalen
dc.contributor.authorCalo, Victor M.en
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorGalvis, Juanen
dc.contributor.authorGhommem, Mehdien
dc.date.accessioned2015-08-12T08:57:58Zen
dc.date.available2015-08-12T08:57:58Zen
dc.date.issued2015-08en
dc.identifier.issn00457825en
dc.identifier.doi10.1016/j.cma.2014.10.034en
dc.identifier.urihttp://hdl.handle.net/10754/565981en
dc.description.abstractIn this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual and the Jacobian on a fine grid. As such, we use local and global empirical interpolation concepts to circumvent performing these computations on the fine grid. The resulting reduced-order approach significantly reduces the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider several numerical examples of nonlinear multiscale partial differential equations that are numerically integrated using fully-implicit time marching schemes to demonstrate the capability of the proposed model reduction approach to speed up simulations of nonlinear flows in high-contrast porous media.en
dc.description.sponsorshipYE's work is partially supported by the US 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, and the grant FA9550-11-1-0341 from the Air Force Office of Scientific Research.en
dc.publisherElsevier BVen
dc.subjectDiscrete empirical interpolationen
dc.subjectGeneralized multiscale finite element methoden
dc.subjectHeterogeneous porous mediaen
dc.subjectNonlinear PDEsen
dc.subjectProper orthogonal decompositionen
dc.titleGlobal-local nonlinear model reduction for flows in heterogeneous porous mediaen
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.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.contributor.institutionDepartment of Mathematics and Institute for Scientific Computation (ISC), Texas A and M University, College Station, TX, USAen
dc.contributor.institutionDepartamento de Matemáticas, Universidad Nacional de Colombia, Carrera 45 No 26-85 - Edificio Uriel Gutierréz, Bogotá D.C., Colombiaen
dc.identifier.arxividarXiv:1407.0782v1en
kaust.authorCalo, Victor M.en
kaust.authorEfendiev, Yalchin R.en
kaust.authorGhommem, Mehdien
kaust.authorAlOtaibi, Manalen
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