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Article: A conservative local multiscale model reduction technique for Stokes flows in heterogeneous perforated domains

TitleA conservative local multiscale model reduction technique for Stokes flows in heterogeneous perforated domains
Authors
KeywordsConservative
Perforated domain
Multiscale model reduction
Stokes flow
Issue Date2017
Citation
Journal of Computational and Applied Mathematics, 2017, v. 321, p. 389-405 How to Cite?
AbstractIn this paper, we present a new multiscale model reduction technique for the Stokes flows in heterogeneous perforated domains. The challenge in the numerical simulations of this problem lies in the fact that the solution contains many multiscale features and requires a very fine mesh to resolve all details. In order to efficiently compute the solutions, some model reductions are necessary. To obtain a reduced model, we apply the generalized multiscale finite element approach, which is a framework allowing systematic construction of reduced models. Based on this general framework, we will first construct a local snapshot space, which contains many possible multiscale features of the solution. Using the snapshot space and a local spectral problem, we identify dominant modes in the snapshot space and use them as the multiscale basis functions. Our basis functions are constructed locally with non-overlapping supports, which enhances the sparsity of the resulting linear system. In order to enforce the mass conservation, we propose a hybridized technique, and uses a Lagrange multiplier to achieve mass conservation. We will mathematically analyze the stability and the convergence of the proposed method. In addition, we will present some numerical examples to show the performance of the scheme. We show that, with a few basis functions per coarse region, one can obtain a solution with excellent accuracy.
Persistent Identifierhttp://hdl.handle.net/10722/303517
ISSN
2020 Impact Factor: 2.621
2020 SCImago Journal Rankings: 0.876
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChung, Eric T.-
dc.contributor.authorVasilyeva, Maria-
dc.contributor.authorWang, Yating-
dc.date.accessioned2021-09-15T08:25:29Z-
dc.date.available2021-09-15T08:25:29Z-
dc.date.issued2017-
dc.identifier.citationJournal of Computational and Applied Mathematics, 2017, v. 321, p. 389-405-
dc.identifier.issn0377-0427-
dc.identifier.urihttp://hdl.handle.net/10722/303517-
dc.description.abstractIn this paper, we present a new multiscale model reduction technique for the Stokes flows in heterogeneous perforated domains. The challenge in the numerical simulations of this problem lies in the fact that the solution contains many multiscale features and requires a very fine mesh to resolve all details. In order to efficiently compute the solutions, some model reductions are necessary. To obtain a reduced model, we apply the generalized multiscale finite element approach, which is a framework allowing systematic construction of reduced models. Based on this general framework, we will first construct a local snapshot space, which contains many possible multiscale features of the solution. Using the snapshot space and a local spectral problem, we identify dominant modes in the snapshot space and use them as the multiscale basis functions. Our basis functions are constructed locally with non-overlapping supports, which enhances the sparsity of the resulting linear system. In order to enforce the mass conservation, we propose a hybridized technique, and uses a Lagrange multiplier to achieve mass conservation. We will mathematically analyze the stability and the convergence of the proposed method. In addition, we will present some numerical examples to show the performance of the scheme. We show that, with a few basis functions per coarse region, one can obtain a solution with excellent accuracy.-
dc.languageeng-
dc.relation.ispartofJournal of Computational and Applied Mathematics-
dc.subjectConservative-
dc.subjectPerforated domain-
dc.subjectMultiscale model reduction-
dc.subjectStokes flow-
dc.titleA conservative local multiscale model reduction technique for Stokes flows in heterogeneous perforated domains-
dc.typeArticle-
dc.description.naturelink_to_OA_fulltext-
dc.identifier.doi10.1016/j.cam.2017.03.004-
dc.identifier.scopuseid_2-s2.0-85016060218-
dc.identifier.volume321-
dc.identifier.spage389-
dc.identifier.epage405-
dc.identifier.isiWOS:000400878000026-

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