Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-10T23:03:38.031Z Has data issue: false hasContentIssue false
  • English
  • Français

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. Gabriel.Barrenechea@inria.fr. Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
Patrick Le Tallec
Affiliation:
École Polytechnique, 91128 Palaiseau Cedex, France. Patrick.LeTallec@polytechnique.fr.
Frédéric Valentin
Affiliation:
LNCC, Av. Getúlio Vargas, 333, 25651-070 Petrópolis - RJ, Brazil. Valentin@lncc.br.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Achdou, Y. and Pironneau, O., Domain decomoposition and wall laws. C. R. Acad. Sci. Paris Série I Math. 320 (1995) 541-547.
Y. Achdou, O. Pironneau and F. Valentin, Etude des lois de paroi d'ordre 1 et 2 pour des domaines rugueux par décomposition de domaine. Technical Report 3326, INRIA (1997).
Achdou, Y., Pironneau, O. and Valentin, F., Effective boundary conditions for laminar flows over periodic rough boundaries. J. Comput. Phys. 147 (1998) 187-218. CrossRef
Y. Achdou, O. Pironneau and F. Valentin, Équations aux dérivées partielles et applications - Articles dédiés à Jacques-Louis Lions, chapter Shape control versus boundary control. Elsevier, Paris (1998) 1-18.
Achdou, Y., Le Tallec, P., Valentin, F. and Pironneau, O., Constructing wall laws with domain decomposition or asymptotic expansion techniques. Comput. Methods Appl. Mech. Engrg. 151 (1998) 215-232. CrossRef
G.R. Barrenechea, Analyse Numérique et Lois de Paroi pour des Écoulements Instationnaires sur des Parois Rugueuses. Ph.D. thesis, Université de Paris Dauphine (2001), in preparation.
A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structures. North Holland (1983).
F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag (1991).
A. Carrau, G. Galice and P. Le Tallec, Taking into account surface roughness in computing hypersonic rentry bodies. Applied Sciences and Engineering, R. Glowinski, Ed., Nova Science publisher (1992) 331-344.
J. Cousteix, Couches Limites Laminaires. Cepadues (1989).
E. Dean and R. Glowinski, 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).
J. Dutton, Dynamics of atmospheric motion. Dover (1986).
Franca, L.P. and Valentin, F., On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation. Comput. Methods Appl. Mech. Engrg. 190 (2000) 1785-1800. CrossRef
V. Girault and P.A. Raviart, Finite Element Methods for the Navier-Stokes Equations. Springer-Verlag (1986).
R. Lewandowski, Analyse mathématique et océanographie. Masson (1997).
Mohammadi, B. and Medic, G., A critical evaluation of the classical k-ε model and wall-laws for unsteady flows over bluff bodies. Int. J. Comput. Fluid Dyn. 10 (1998) 1-11. CrossRef
Mohammadi, B. and Pironneau, O., Unsteady separated turbulent flows computation with wall-laws and k-ε model. Comput. Methods Appl. Mech. Engrg. 148 (1997) 393-405. CrossRef
E. Sánchez-Palencia, 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.
Smith, A. and Silvester, D., Implicit algorithms and their linearization for the transient incompressible Navier-Stokes equations. IMA J. Numer. Anal. 17 (1997) 527-545. CrossRef
R. Temam, Navier Stokes Equations. Theory and Numerical Algorithms. North-Holland, third edition (1984).
F. Valentin, 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).
T. Yamaguchi, Computational mechanics simulation for clinical cardiovascular medicine, in ECCOMAS 2000, Barcelona (2000).