A note on variational multiscale methods for high-contrast heterogeneous porous media flows with rough source terms

Handle URI:
http://hdl.handle.net/10754/561860
Title:
A note on variational multiscale methods for high-contrast heterogeneous porous media flows with rough source terms
Authors:
Calo, Victor M. ( 0000-0002-1805-4045 ) ; Efendiev, Yalchin R.; Galvis, Juan
Abstract:
In this short note, we discuss variational multiscale methods for solving porous media flows in high-contrast heterogeneous media with rough source terms. Our objective is to separate, as much as possible, subgrid effects induced by the media properties from those due to heterogeneous source terms. For this reason, enriched coarse spaces designed for high-contrast multiscale problems are used to represent the effects of heterogeneities of the media. Furthermore, rough source terms are captured via auxiliary correction equations that appear in the formulation of variational multiscale methods [23]. These auxiliary equations are localized and one can use additive or multiplicative constructions for the subgrid corrections as discussed in the current paper. Our preliminary numerical results show that one can capture the effects due to both spatial heterogeneities in the coefficients (such as permeability field) and source terms (e.g., due to singular well terms) in one iteration. We test the cases for both smooth source terms and rough source terms and show that with the multiplicative correction, the numerical approximations are more accurate compared to the additive correction. © 2010 Elsevier Ltd.
KAUST Department:
Applied Mathematics and Computational Science Program; Earth Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Numerical Porous Media SRI Center (NumPor)
Publisher:
Elsevier BV
Journal:
Advances in Water Resources
Issue Date:
Sep-2011
DOI:
10.1016/j.advwatres.2010.12.011
Type:
Article
ISSN:
03091708
Sponsors:
This work is partially supported by Award Number KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). YE's research was partially supported by the DOE and NSF (DMS 0934837, DMS0621113, DMS 0724704, DMR-0844082, and DMS 0811180).
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

Full metadata record

DC FieldValue Language
dc.contributor.authorCalo, Victor M.en
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorGalvis, Juanen
dc.date.accessioned2015-08-03T09:32:42Zen
dc.date.available2015-08-03T09:32:42Zen
dc.date.issued2011-09en
dc.identifier.issn03091708en
dc.identifier.doi10.1016/j.advwatres.2010.12.011en
dc.identifier.urihttp://hdl.handle.net/10754/561860en
dc.description.abstractIn this short note, we discuss variational multiscale methods for solving porous media flows in high-contrast heterogeneous media with rough source terms. Our objective is to separate, as much as possible, subgrid effects induced by the media properties from those due to heterogeneous source terms. For this reason, enriched coarse spaces designed for high-contrast multiscale problems are used to represent the effects of heterogeneities of the media. Furthermore, rough source terms are captured via auxiliary correction equations that appear in the formulation of variational multiscale methods [23]. These auxiliary equations are localized and one can use additive or multiplicative constructions for the subgrid corrections as discussed in the current paper. Our preliminary numerical results show that one can capture the effects due to both spatial heterogeneities in the coefficients (such as permeability field) and source terms (e.g., due to singular well terms) in one iteration. We test the cases for both smooth source terms and rough source terms and show that with the multiplicative correction, the numerical approximations are more accurate compared to the additive correction. © 2010 Elsevier Ltd.en
dc.description.sponsorshipThis work is partially supported by Award Number KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). YE's research was partially supported by the DOE and NSF (DMS 0934837, DMS0621113, DMS 0724704, DMR-0844082, and DMS 0811180).en
dc.publisherElsevier BVen
dc.subjectHeterogeneousen
dc.subjectHigh-contrasten
dc.subjectMultiscaleen
dc.subjectMultiscale finite elementen
dc.subjectSourceen
dc.subjectVariational multiscaleen
dc.titleA note on variational multiscale methods for high-contrast heterogeneous porous media flows with rough source termsen
dc.typeArticleen
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.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalAdvances in Water Resourcesen
dc.contributor.institutionDepartment of Mathematics, Texas A and M University, College Station, TX 77843, United Statesen
kaust.authorCalo, Victor M.en
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