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.
Classification: 76M45, 76M10
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {36},
number = {2},
year = {2002},
pages = {177-203},
doi = {10.1051/m2an:2002009},
zbl = {1040.76009},
mrnumber = {1906814},
language = {en},
url = {http://www.numdam.org/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 2, pp. 177-203. doi : 10.1051/m2an:2002009. http://www.numdam.org/item/M2AN_2002__36_2_177_0/
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