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Article: Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations

TitleNonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations
Authors
KeywordsCEM-GMsFEM
Multiscale
Partially explicit
Porous media
Transport equations
Issue Date2023
Citation
Journal of Computational Physics, 2023, v. 472, article no. 111555 How to Cite?
AbstractIn this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equations in heterogeneous media and play an important role in many applications. First, we present a dememorization technique for these equations. We show that the convection-diffusion equations with memory effects can be written as a system of standard convection diffusion reaction equations. This allows removing the memory term and simplifying the computations. We consider a relation between dememorized equations and micro-scale equations, which do not contain memory terms. We note that dememorized equations differ from micro-scale equations and constitute a macroscopic model. Next, we consider both implicit and partially explicit methods. The latter is introduced for problems in multiscale media with high-contrast properties. Because of high-contrast, explicit methods are restrictive and require time steps that are very small (scales as the inverse of the contrast). We show that, by appropriately decomposing the space, we can treat only a few degrees of freedom implicitly and the remaining degrees of freedom explicitly. We present a stability analysis. Numerical results are presented that confirm our theoretical findings about partially explicit schemes applied to dememorized systems of equations.
Persistent Identifierhttp://hdl.handle.net/10722/327683
ISSN
2023 Impact Factor: 3.8
2023 SCImago Journal Rankings: 1.679
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorEfendiev, Yalchin-
dc.contributor.authorLeung, Wing Tat-
dc.contributor.authorLi, Wenyuan-
dc.contributor.authorPun, Sai Mang-
dc.contributor.authorVabishchevich, Petr N.-
dc.date.accessioned2023-04-12T04:05:02Z-
dc.date.available2023-04-12T04:05:02Z-
dc.date.issued2023-
dc.identifier.citationJournal of Computational Physics, 2023, v. 472, article no. 111555-
dc.identifier.issn0021-9991-
dc.identifier.urihttp://hdl.handle.net/10722/327683-
dc.description.abstractIn this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equations in heterogeneous media and play an important role in many applications. First, we present a dememorization technique for these equations. We show that the convection-diffusion equations with memory effects can be written as a system of standard convection diffusion reaction equations. This allows removing the memory term and simplifying the computations. We consider a relation between dememorized equations and micro-scale equations, which do not contain memory terms. We note that dememorized equations differ from micro-scale equations and constitute a macroscopic model. Next, we consider both implicit and partially explicit methods. The latter is introduced for problems in multiscale media with high-contrast properties. Because of high-contrast, explicit methods are restrictive and require time steps that are very small (scales as the inverse of the contrast). We show that, by appropriately decomposing the space, we can treat only a few degrees of freedom implicitly and the remaining degrees of freedom explicitly. We present a stability analysis. Numerical results are presented that confirm our theoretical findings about partially explicit schemes applied to dememorized systems of equations.-
dc.languageeng-
dc.relation.ispartofJournal of Computational Physics-
dc.subjectCEM-GMsFEM-
dc.subjectMultiscale-
dc.subjectPartially explicit-
dc.subjectPorous media-
dc.subjectTransport equations-
dc.titleNonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.jcp.2022.111555-
dc.identifier.scopuseid_2-s2.0-85140091855-
dc.identifier.volume472-
dc.identifier.spagearticle no. 111555-
dc.identifier.epagearticle no. 111555-
dc.identifier.eissn1090-2716-
dc.identifier.isiWOS:000879217600015-

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