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.
Mots clés : Wall law, unsteady Navier-Stokes equations, asymptotic analysis, rough boundary
@article{M2AN_2002__36_2_177_0,
author = {Barrenechea, Gabriel R. and Tallec, Patrick Le and Valentin, Fr\'ed\'eric},
title = {New wall laws for the unsteady incompressible {Navier-Stokes} equations on rough domains},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {177--203},
publisher = {EDP-Sciences},
volume = {36},
number = {2},
year = {2002},
doi = {10.1051/m2an:2002009},
mrnumber = {1906814},
zbl = {1040.76009},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2002009/}
}
TY - JOUR AU - Barrenechea, Gabriel R. AU - Tallec, Patrick Le AU - Valentin, Frédéric TI - New wall laws for the unsteady incompressible Navier-Stokes equations on rough domains JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2002 SP - 177 EP - 203 VL - 36 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2002009/ DO - 10.1051/m2an:2002009 LA - en ID - M2AN_2002__36_2_177_0 ER -
%0 Journal Article %A Barrenechea, Gabriel R. %A Tallec, Patrick Le %A Valentin, Frédéric %T New wall laws for the unsteady incompressible Navier-Stokes equations on rough domains %J ESAIM: Modélisation mathématique et analyse numérique %D 2002 %P 177-203 %V 36 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2002009/ %R 10.1051/m2an:2002009 %G en %F M2AN_2002__36_2_177_0
Barrenechea, Gabriel R.; Tallec, Patrick Le; Valentin, Frédéric. New wall laws for the unsteady incompressible Navier-Stokes equations on rough domains. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 2, pp. 177-203. doi : 10.1051/m2an:2002009. http://www.numdam.org/articles/10.1051/m2an:2002009/
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