Asymptotic analysis for micropolar fluids

Delphine Dupuy; Gregory P. Panasenko; Ruxandra Stavre

doi:10.1016/j.crme.2003.10.013

Asymptotic analysis for micropolar fluids

Presented by: Évariste Sanchez-Palencia

Delphine Dupuy ¹; Gregory P. Panasenko ^1,²; Ruxandra Stavre ³

¹ Équipe d'analyse numérique, UPRES EA 3058, Université de Saint-Etienne, 23, rue Paul Michelon, 42023 Saint-Etienne, France
² Laboratoire de modélisation en mécanique – CNRS UMR 7607, Université Pierre et Marie Curie – Paris VI, 8, rue du Capitaine Scott, 75015 Paris, France
³ Institute of Mathematics “Simion Stoilow” Romanian Academy, PO Box 1-764, 70700 Bucharest, Romania

Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 31-36.

Abstract
Résumé

The flow of a micropolar fluid through a wavy constricted channel which depends on a small parameter ε⪡1 is considered. The asymptotic solution is built and justified thanks to a study of the boundary layers terms. The Stokes and Navier–Stokes problems set in a tube structure were previously considered. The method of partial asymptotic decomposition of domain (MAPPD) is also applied and justified for the micropolar flow problem. This method reduces the initial problem to the problem set in the boundary layers domain.

Cet article porte sur l'étude de l'écoulement d'un fluide micropolaire à l'intérieur d'un tube, périodiquement ondulé, de période ε, de largeur d'ordre ε et de longueur d'ordre 1. En utilisant une étude similaire à celle effectuée pour des écoulements de Stokes et de Navier–Stokes dans une structure tubulaire, on considère une analyse asymptotique de ce problème. Une solution asymptotique est construite et les termes de couche limite qui apparaissent au voisinage des extrémités sont étudiés. Après justification de cette approche, la méthode de décomposition asymptotique partielle du domaine est mise en place pour ce problème.

Received: 2003-09-25
Accepted: 2003-10-21
Published online: 2003-12-21

DOI: 10.1016/j.crme.2003.10.013

Keywords: Computational fluid mechanics, Micropolar fluids, Asymptotic expansion, Partial asymptotic domain decomposition
Mots-clés : Mécanique des fluides numérique, Fluides micropolaires, Dévéloppement asymptotique, Décomposition asymptotique partielle du domaine

Author's affiliations:

Delphine Dupuy ¹; Gregory P. Panasenko ^{1, 2}; Ruxandra Stavre ³

¹ Équipe d'analyse numérique, UPRES EA 3058, Université de Saint-Etienne, 23, rue Paul Michelon, 42023 Saint-Etienne, France
² Laboratoire de modélisation en mécanique – CNRS UMR 7607, Université Pierre et Marie Curie – Paris VI, 8, rue du Capitaine Scott, 75015 Paris, France
³ Institute of Mathematics “Simion Stoilow” Romanian Academy, PO Box 1-764, 70700 Bucharest, Romania

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     title = {Asymptotic analysis for micropolar fluids},
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Delphine Dupuy; Gregory P. Panasenko; Ruxandra Stavre. Asymptotic analysis for micropolar fluids. Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 31-36. doi : 10.1016/j.crme.2003.10.013. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.10.013/

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