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Article: Multiscale model reduction for transport and flow problems in perforated domains

TitleMultiscale model reduction for transport and flow problems in perforated domains
Authors
KeywordsMultiscale model reduction
Flow and transport
Perforated domains
Issue Date2018
Citation
Journal of Computational and Applied Mathematics, 2018, v. 330, p. 519-535 How to Cite?
AbstractConvection-dominated transport phenomenon is important for many applications. In these applications, the transport velocity is often a solution of heterogeneous flow problems, which results to a coupled flow and transport phenomena. In this paper, we consider a coupled flow (Stokes problem) and transport (unsteady convection–diffusion problem) in perforated domains. Perforated domains (see Fig. 1) represent void space outside hard inclusions as in porous media, filters, and so on. We construct a coarse-scale solver based on Generalized Multiscale Finite Element Method (GMsFEM) for a coupled flow and transport. The main idea of the GMsFEM is to develop a systematic approach for computing multiscale basis functions. We use a mixed formulation and appropriate multiscale basis functions for both flow and transport to guarantee a mass conservation. For the transport problem, we use Petrov–Galerkin mixed formulation, which provides a stability. As a first approach, we use the multiscale flow solution in constructing the basis functions for the transport equation. In the second approach, we construct multiscale basis functions for coupled flow and transport without solving global flow problem. The novelty of this approach is to construct a coupled multiscale basis function. Numerical results are presented for computations using offline basis. We also present an algorithm for adaptively adding online multiscale basis functions, which are computed using the residual information. Numerical examples using online GMsFEM show the speed up of convergence.
Persistent Identifierhttp://hdl.handle.net/10722/303541
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.authorLeung, Wing Tat-
dc.contributor.authorVasilyeva, Maria-
dc.contributor.authorWang, Yating-
dc.date.accessioned2021-09-15T08:25:32Z-
dc.date.available2021-09-15T08:25:32Z-
dc.date.issued2018-
dc.identifier.citationJournal of Computational and Applied Mathematics, 2018, v. 330, p. 519-535-
dc.identifier.issn0377-0427-
dc.identifier.urihttp://hdl.handle.net/10722/303541-
dc.description.abstractConvection-dominated transport phenomenon is important for many applications. In these applications, the transport velocity is often a solution of heterogeneous flow problems, which results to a coupled flow and transport phenomena. In this paper, we consider a coupled flow (Stokes problem) and transport (unsteady convection–diffusion problem) in perforated domains. Perforated domains (see Fig. 1) represent void space outside hard inclusions as in porous media, filters, and so on. We construct a coarse-scale solver based on Generalized Multiscale Finite Element Method (GMsFEM) for a coupled flow and transport. The main idea of the GMsFEM is to develop a systematic approach for computing multiscale basis functions. We use a mixed formulation and appropriate multiscale basis functions for both flow and transport to guarantee a mass conservation. For the transport problem, we use Petrov–Galerkin mixed formulation, which provides a stability. As a first approach, we use the multiscale flow solution in constructing the basis functions for the transport equation. In the second approach, we construct multiscale basis functions for coupled flow and transport without solving global flow problem. The novelty of this approach is to construct a coupled multiscale basis function. Numerical results are presented for computations using offline basis. We also present an algorithm for adaptively adding online multiscale basis functions, which are computed using the residual information. Numerical examples using online GMsFEM show the speed up of convergence.-
dc.languageeng-
dc.relation.ispartofJournal of Computational and Applied Mathematics-
dc.subjectMultiscale model reduction-
dc.subjectFlow and transport-
dc.subjectPerforated domains-
dc.titleMultiscale model reduction for transport and flow problems in perforated domains-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.cam.2017.08.017-
dc.identifier.scopuseid_2-s2.0-85030325819-
dc.identifier.volume330-
dc.identifier.spage519-
dc.identifier.epage535-
dc.identifier.isiWOS:000415783000037-

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