Geodesic
New wall laws for the unsteady incompressible Navier-Stokes equations on rough domains
Barrenechea, Gabriel R.  ; Le Tallec, Patrick 1  ; Valentin, Frédéric
1 Ecole Polytechnique, 91128 Palaiseau Cedex, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 36 (2002) no. 2, pp. 177-203

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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.

DOI : 10.1051/m2an:2002009
Classification : 76M45, 76M10
Keywords: Wall law, unsteady Navier-Stokes equations, asymptotic analysis, rough boundary

Barrenechea, Gabriel R.  ; Le Tallec, Patrick  1 ; Valentin, Frédéric 

1 Ecole Polytechnique, 91128 Palaiseau Cedex, France. 
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     title = {New wall laws for the unsteady incompressible {Navier-Stokes} equations on rough domains},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {177--203},
     publisher = {EDP-Sciences},
     volume = {36},
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     year = {2002},
     doi = {10.1051/m2an:2002009},
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     zbl = {1040.76009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2002009/}
}
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Barrenechea, Gabriel R.; Le Tallec, Patrick ; Valentin, Frédéric. New wall laws for the unsteady incompressible Navier-Stokes equations on rough domains. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 36 (2002) no. 2, pp. 177-203. doi: 10.1051/m2an:2002009

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