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dc.creatorNarbona Reina, Gladys
dc.creatorBresch, Didier
dc.date.accessioned2016-01-12T13:56:02Z
dc.date.available2016-01-12T13:56:02Z
dc.date.issued2013
dc.identifier.citationNarbona-Reina, G. y Bresch, D. (2013). Two shallow-water type models for viscoelastic flows from kinetic theory for polymers solutions. ESAIM: Mathematical modelling and numerical analysis, 47, 1627-1655.es
dc.identifier.issn1290-3841es
dc.identifier.urihttp://hdl.handle.net/11441/32422
dc.description.abstractIn this work, depending on the relation between the Deborah, the Reynolds and the aspect ratio numbers, we formally derived shallow-water type systems starting from a micro-macro description for non-Newtonian fluids in a thin domain governed by an elastic dumbbell type model with a slip boundary condition at the bottom. The result has been announced by the authors in [G. Narbona-Reina, D. Bresch, Numer. Math. and Advanced Appl. Springer Verlag (2010)] and in the present paper, we provide a self-contained description, complete formal derivations and various numerical computations. In particular, we extend to FENE type systems the derivation of shallowwater models for Newtonian fluids that we can find for instance in [J.-F. Gerbeau, B. Perthame, Discrete Contin. Dyn. Syst. (2001)] which assume an appropriate relation between the Reynolds number and the aspect ratio with slip boundary condition at the bottom. Under a radial hypothesis at the leading order, for small Deborah number, we find an interesting formulation where polymeric effect changes the drag term in the second order shallow-water formulation (obtained by J.-F. Gerbeau, B. Perthame). We also discuss intermediate Deborah number with a fixed Reynolds number where a strong coupling is found through a nonlinear time-dependent Fokker–Planck equation. This generalizes, at a formal level, the derivation in [L. Chupin, Meth. Appl. Anal. (2009)] including non-linear effects (shallow-water framework).es
dc.formatapplication/pdfes
dc.language.isoenges
dc.publisherDunodes
dc.relation.ispartofESAIM: Mathematical modelling and numerical analysis, 47, 1627-1655es
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.titleTwo shallow-water type models for viscoelastic flows from kinetic theory for polymers solutionses
dc.typeinfo:eu-repo/semantics/articlees
dcterms.identifierhttps://ror.org/03yxnpp24
dc.type.versioninfo:eu-repo/semantics/publishedVersiones
dc.rights.accessrightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)es
dc.identifier.doihttp://dx.doi.org/10.1051/m2an/2013081es
dc.journaltitleESAIM: Mathematical modelling and numerical analysises
dc.publication.volumen47es
dc.publication.initialPage1627es
dc.publication.endPage1655es
dc.identifier.idushttps://idus.us.es/xmlui/handle/11441/32422

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