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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v5.i6.40
pages 473-482

Asymptotic and Numerical Modeling of a Flow in a Thin Channel with Viscoelastic Wall

Gregory P. Panasenko
Equipe d'Analise Numerique UMR CNRS 5585, University Gean Monnet 23 rue. P. Michelon 42023 St. Etienne, France
Y. Sirakov
Laboratory of Rheology for Plastic Materials of the University of Saint-Etienne (UMR CNRS 5156), University Jean Monnet, 42023 Saint-Etienne, France
R. Stavre
Institute of Mathematics "Simion Stoilow", Romanian Academy, P.O. Box 1-764 RO-70700 Bucharest, Romania

ABSTRACT

This article deals with a theoretical and numerical study of a fluid-structure interaction problem. We consider the nonstationary flow of a viscous fluid in a thin rectangle with an elastic wall as the upper part of the boundary. The physical problem that corresponds to nonhomogeneous boundary conditions is stated. By using a boundary layer method, an asymptotic solution is constructed. The properties of the boundary layer functions are established, and an error estimate is obtained. The asymptotic expansions are justified both by the error estimates and by the numerical simulations.


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