Hierarchical multiscale modeling for flows in fractured media using generalized multiscale finite element method

Handle URI:
http://hdl.handle.net/10754/622202
Title:
Hierarchical multiscale modeling for flows in fractured media using generalized multiscale finite element method
Authors:
Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Lee, Seong; Li, Guanglian; Yao, Jun; Zhang, Na
Abstract:
In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on generalized multiscale finite element method (GMsFEM), where we represent the fracture effects on a coarse grid via multiscale basis functions. These multiscale basis functions are constructed in the offline stage via local spectral problems following GMsFEM. To represent the fractures on the fine grid, we consider two approaches (1) discrete fracture model (DFM) (2) embedded fracture model (EFM) and their combination. In DFM, the fractures are resolved via the fine grid, while in EFM the fracture and the fine grid block interaction is represented as a source term. In the proposed multiscale method, additional multiscale basis functions are used to represent the long fractures, while short-size fractures are collectively represented by a single basis functions. The procedure is automatically done via local spectral problems. In this regard, our approach shares common concepts with several approaches proposed in the literature as we discuss. We would like to emphasize that our goal is not to compare DFM with EFM, but rather to develop GMsFEM framework which uses these (DFM or EFM) fine-grid discretization techniques. Numerical results are presented, where we demonstrate how one can adaptively add basis functions in the regions of interest based on error indicators. We also discuss the use of randomized snapshots (Calo et al. Randomized oversampling for generalized multiscale finite element methods, 2014), which reduces the offline computational cost.
KAUST Department:
Numerical Porous Media SRI Center (NumPor)
Citation:
Efendiev Y, Lee S, Li G, Yao J, Zhang N (2015) Hierarchical multiscale modeling for flows in fractured media using generalized multiscale finite element method. GEM - International Journal on Geomathematics 6: 141–162. Available: http://dx.doi.org/10.1007/s13137-015-0075-7.
Publisher:
Springer Science + Business Media
Journal:
GEM - International Journal on Geomathematics
Issue Date:
5-Jun-2015
DOI:
10.1007/s13137-015-0075-7
Type:
Article
ISSN:
1869-2672; 1869-2680
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorLee, Seongen
dc.contributor.authorLi, Guanglianen
dc.contributor.authorYao, Junen
dc.contributor.authorZhang, Naen
dc.date.accessioned2017-01-02T08:42:37Z-
dc.date.available2017-01-02T08:42:37Z-
dc.date.issued2015-06-05en
dc.identifier.citationEfendiev Y, Lee S, Li G, Yao J, Zhang N (2015) Hierarchical multiscale modeling for flows in fractured media using generalized multiscale finite element method. GEM - International Journal on Geomathematics 6: 141–162. Available: http://dx.doi.org/10.1007/s13137-015-0075-7.en
dc.identifier.issn1869-2672en
dc.identifier.issn1869-2680en
dc.identifier.doi10.1007/s13137-015-0075-7en
dc.identifier.urihttp://hdl.handle.net/10754/622202-
dc.description.abstractIn this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on generalized multiscale finite element method (GMsFEM), where we represent the fracture effects on a coarse grid via multiscale basis functions. These multiscale basis functions are constructed in the offline stage via local spectral problems following GMsFEM. To represent the fractures on the fine grid, we consider two approaches (1) discrete fracture model (DFM) (2) embedded fracture model (EFM) and their combination. In DFM, the fractures are resolved via the fine grid, while in EFM the fracture and the fine grid block interaction is represented as a source term. In the proposed multiscale method, additional multiscale basis functions are used to represent the long fractures, while short-size fractures are collectively represented by a single basis functions. The procedure is automatically done via local spectral problems. In this regard, our approach shares common concepts with several approaches proposed in the literature as we discuss. We would like to emphasize that our goal is not to compare DFM with EFM, but rather to develop GMsFEM framework which uses these (DFM or EFM) fine-grid discretization techniques. Numerical results are presented, where we demonstrate how one can adaptively add basis functions in the regions of interest based on error indicators. We also discuss the use of randomized snapshots (Calo et al. Randomized oversampling for generalized multiscale finite element methods, 2014), which reduces the offline computational cost.en
dc.publisherSpringer Science + Business Mediaen
dc.subjectDiscrete fracture modelen
dc.subjectFractured mediaen
dc.subjectGMsFEMen
dc.subjectMultiscale finite elementen
dc.titleHierarchical multiscale modeling for flows in fractured media using generalized multiscale finite element methoden
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalGEM - International Journal on Geomathematicsen
dc.contributor.institutionDepartment of Mathematics and Institute for Scientific Computation (ISC), Texas A&M University, College Station, TX, United Statesen
dc.contributor.institutionChevron ETC, Houston, TX, 77002, United Statesen
dc.contributor.institutionDepartment of Mathematics, Texas A&M University, College Station, TX, 77843-3368, United Statesen
dc.contributor.institutionSchool of Petroleum Engineering, China University of Petroleum (East China), Qingdao, Shandong, 266555, Chinaen
kaust.authorEfendiev, Yalchin R.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.