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 Le Tallec, Patrick 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://archive.numdam.org/articles/10.1051/m2an:2002009/}
}
TY - JOUR AU - Barrenechea, Gabriel R. AU - Le Tallec, Patrick 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://archive.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 Le Tallec, Patrick %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://archive.numdam.org/articles/10.1051/m2an:2002009/ %R 10.1051/m2an:2002009 %G en %F M2AN_2002__36_2_177_0
Barrenechea, Gabriel R.; Le Tallec, Patrick ; 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://archive.numdam.org/articles/10.1051/m2an:2002009/
[1] and, Domain decomoposition and wall laws. C. R. Acad. Sci. Paris Série I Math. 320 (1995) 541-547. | Zbl
[2] , and, Etude des lois de paroi d'ordre 1 et 2 pour des domaines rugueux par décomposition de domaine. Technical Report 3326, INRIA (1997).
[3] , and, Effective boundary conditions for laminar flows over periodic rough boundaries. J. Comput. Phys. 147 (1998) 187-218. | Zbl
[4] , and, Équations aux dérivées partielles et applications - Articles dédiés à Jacques-Louis Lions, chapter Shape control versus boundary control. Elsevier, Paris (1998) 1-18. | Zbl
[5] ,, and, Constructing wall laws with domain decomposition or asymptotic expansion techniques. Comput. Methods Appl. Mech. Engrg. 151 (1998) 215-232. | Zbl
[6] , Analyse Numérique et Lois de Paroi pour des Écoulements Instationnaires sur des Parois Rugueuses. Ph.D. thesis, Université de Paris Dauphine (2001), in preparation.
[7] , and, Asymptotic analysis for periodic structures. North Holland (1983). | MR | Zbl
[8] and, Mixed and Hybrid Finite Element Methods. Springer-Verlag (1991). | MR | Zbl
[9] , and, Taking into account surface roughness in computing hypersonic rentry bodies. Applied Sciences and Engineering, R. Glowinski, Ed., Nova Science publisher (1992) 331-344.
[10] , Couches Limites Laminaires. Cepadues (1989).
[11] and, On some finite element methods for the numerical solution of incompressible flow, in Incompressible Computational Fluid Dynamics, M. Gunzburger and R. Nicolaides, Eds., Cambridge University Press (1993).
[12] , Dynamics of atmospheric motion. Dover (1986).
[13] and, On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation. Comput. Methods Appl. Mech. Engrg. 190 (2000) 1785-1800. | Zbl
[14] and, Finite Element Methods for the Navier-Stokes Equations. Springer-Verlag (1986). | MR | Zbl
[15] , Analyse mathématique et océanographie. Masson (1997).
[16] and, A critical evaluation of the classical k- model and wall-laws for unsteady flows over bluff bodies. Int. J. Comput. Fluid Dyn. 10 (1998) 1-11. | Zbl
[17] and, Unsteady separated turbulent flows computation with wall-laws and k- model. Comput. Methods Appl. Mech. Engrg. 148 (1997) 393-405. | Zbl
[18] , Un problème d'écoulement lent d'un fluide visqueux incompressible au travers d'une paroi finement perforée, in Les Méthodes de l'Homogénéisation: Théorie et Applications en Physique, D. Bergman et coll, Eds., Vol. 57 of Collection de la Direction des Études et Recherche d'Électricité de France, Eyrolles, Paris (1985) 371-400.
[19] and, Implicit algorithms and their linearization for the transient incompressible Navier-Stokes equations. IMA J. Numer. Anal. 17 (1997) 527-545. | Zbl
[20] , Navier Stokes Equations. Theory and Numerical Algorithms. North-Holland, third edition (1984). | MR | Zbl
[21] , Nouvelles conditions aux limites équivalentes pour des interfaces rugueuses en mécanique des fluides : développement, analyse et mise en ouvre numérique. Ph.D. thesis, Université Paris 6 (1998).
[22] , Computational mechanics simulation for clinical cardiovascular medicine, in ECCOMAS 2000, Barcelona (2000).
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