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New Wall Laws for the Unsteady Incompressible Navier-Stokes Equations on Rough Domains

Published online by Cambridge University Press:  15 May 2002

Gabriel R. Barrenechea ,
Patrick Le Tallec  and
Frédéric Valentin
Gabriel R. Barrenechea
Affiliation:
INRIA Projet M3N, Domaine de Voluceau, 78153 Le Chesnay, France. [email protected]. Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
Patrick Le Tallec
Affiliation:
École Polytechnique, 91128 Palaiseau Cedex, France. [email protected].
Frédéric Valentin
Affiliation:
LNCC, Av. Getúlio Vargas, 333, 25651-070 Petrópolis - RJ, Brazil. [email protected].
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Abstract

Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic expansion techniques. The roughness elements are supposed to be periodic and the influence of the rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady Stokes problems and so they are calculated only once. Numerical tests are presented to validate and compare the proposed boundary conditions.

Keywords

Wall lawunsteady Navier-Stokes equationsasymptotic analysisrough boundary.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 2 , March 2002 , pp. 177 - 203
Copyright
© EDP Sciences, SMAI, 2002

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