A generalized multiscale finite element method for elastic wave propagation in fractured media

Handle URI:
http://hdl.handle.net/10754/622163
Title:
A generalized multiscale finite element method for elastic wave propagation in fractured media
Authors:
Chung, Eric T.; Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Gibson, Richard L.; Vasilyeva, Maria
Abstract:
In this paper, we consider elastic wave propagation in fractured media applying a linear-slip model to represent the effects of fractures on the wavefield. Fractured media, typically, are highly heterogeneous due to multiple length scales. Direct numerical simulations for wave propagation in highly heterogeneous fractured media can be computationally expensive and require some type of model reduction. We develop a multiscale model reduction technique that captures the complex nature of the media (heterogeneities and fractures) in the coarse scale system. The proposed method is based on the generalized multiscale finite element method, where the multiscale basis functions are constructed to capture the fine-scale information of the heterogeneous, fractured media and effectively reduce the degrees of freedom. These multiscale basis functions are coupled via the interior penalty discontinuous Galerkin method, which provides a block-diagonal mass matrix. The latter is needed for fast computation in an explicit time discretization, which is used in our simulations. Numerical results are presented to show the performance of the presented multiscale method for fractured media. We consider several cases where fractured media contain fractures of multiple lengths. Our numerical results show that the proposed reduced-order models can provide accurate approximations for the fine-scale solution.
KAUST Department:
Numerical Porous Media SRI Center (NumPor)
Citation:
Chung ET, Efendiev Y, Gibson RL, Vasilyeva M (2016) A generalized multiscale finite element method for elastic wave propagation in fractured media. GEM - International Journal on Geomathematics 7: 163–182. Available: http://dx.doi.org/10.1007/s13137-016-0081-4.
Publisher:
Springer Nature
Journal:
GEM - International Journal on Geomathematics
Issue Date:
26-Feb-2016
DOI:
10.1007/s13137-016-0081-4
Type:
Article
ISSN:
1869-2672; 1869-2680
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorChung, Eric T.en
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorGibson, Richard L.en
dc.contributor.authorVasilyeva, Mariaen
dc.date.accessioned2017-01-02T08:42:35Z-
dc.date.available2017-01-02T08:42:35Z-
dc.date.issued2016-02-26en
dc.identifier.citationChung ET, Efendiev Y, Gibson RL, Vasilyeva M (2016) A generalized multiscale finite element method for elastic wave propagation in fractured media. GEM - International Journal on Geomathematics 7: 163–182. Available: http://dx.doi.org/10.1007/s13137-016-0081-4.en
dc.identifier.issn1869-2672en
dc.identifier.issn1869-2680en
dc.identifier.doi10.1007/s13137-016-0081-4en
dc.identifier.urihttp://hdl.handle.net/10754/622163-
dc.description.abstractIn this paper, we consider elastic wave propagation in fractured media applying a linear-slip model to represent the effects of fractures on the wavefield. Fractured media, typically, are highly heterogeneous due to multiple length scales. Direct numerical simulations for wave propagation in highly heterogeneous fractured media can be computationally expensive and require some type of model reduction. We develop a multiscale model reduction technique that captures the complex nature of the media (heterogeneities and fractures) in the coarse scale system. The proposed method is based on the generalized multiscale finite element method, where the multiscale basis functions are constructed to capture the fine-scale information of the heterogeneous, fractured media and effectively reduce the degrees of freedom. These multiscale basis functions are coupled via the interior penalty discontinuous Galerkin method, which provides a block-diagonal mass matrix. The latter is needed for fast computation in an explicit time discretization, which is used in our simulations. Numerical results are presented to show the performance of the presented multiscale method for fractured media. We consider several cases where fractured media contain fractures of multiple lengths. Our numerical results show that the proposed reduced-order models can provide accurate approximations for the fine-scale solution.en
dc.publisherSpringer Natureen
dc.subjectFracturesen
dc.subjectHeterogeneousen
dc.subjectMultiscale finite element methoden
dc.subjectWave propagationen
dc.titleA generalized multiscale finite element method for elastic wave propagation in fractured mediaen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalGEM - International Journal on Geomathematicsen
dc.contributor.institutionDepartment of Mathematics, The Chinese University of Hong Kong (CUHK), Sha Tin, Hong Kongen
dc.contributor.institutionDepartment of Mathematics, Institute for Scientific Computation (ISC), Texas A&M University, College Station, TX, United Statesen
dc.contributor.institutionDepartment of Geology and Geophysics, Texas A&M University, College Station, TX, 77843, United Statesen
dc.contributor.institutionDepartment of Computational Technologies, Institute of Mathematics and Informatics, North-Eastern Federal University, Yakutsk, Republic of Sakha (Yakutia), 677980, Russian Federationen
dc.contributor.institutionInstitute for Scientific Computation, Texas A&M University, College Station, TX, 77843-3368, United Statesen
kaust.authorEfendiev, Yalchin R.en
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