New Wall Laws for the Unsteady Incompressible Navier-Stokes Equations on Rough Domains

Gabriel R. Barrenechea; Patrick Le Tallec; Frédéric Valentin

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 36, Issue: 2, page 177-203
  • ISSN: 0764-583X

Abstract

top
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.

How to cite

top

Barrenechea, Gabriel R., Le Tallec, Patrick, and Valentin, Frédéric. "New Wall Laws for the Unsteady Incompressible Navier-Stokes Equations on Rough Domains." ESAIM: Mathematical Modelling and Numerical Analysis 36.2 (2010): 177-203. <http://eudml.org/doc/194100>.

@article{Barrenechea2010,
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. },
author = {Barrenechea, Gabriel R., Le Tallec, Patrick, Valentin, Frédéric},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Wall law; unsteady Navier-Stokes equations; asymptotic analysis; rough boundary.; rough boundary; two-scale asymptotic expansion},
language = {eng},
month = {3},
number = {2},
pages = {177-203},
publisher = {EDP Sciences},
title = {New Wall Laws for the Unsteady Incompressible Navier-Stokes Equations on Rough Domains},
url = {http://eudml.org/doc/194100},
volume = {36},
year = {2010},
}

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: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 2
SP - 177
EP - 203
AB - 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.
LA - eng
KW - Wall law; unsteady Navier-Stokes equations; asymptotic analysis; rough boundary.; rough boundary; two-scale asymptotic expansion
UR - http://eudml.org/doc/194100
ER -

References

top
  1. Y. Achdou and O. Pironneau, Domain decomoposition and wall laws. C. R. Acad. Sci. Paris Série I Math.320 (1995) 541-547.  
  2. 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).  
  3. Y. Achdou, O. Pironneau and F. Valentin, Effective boundary conditions for laminar flows over periodic rough boundaries. J. Comput. Phys.147 (1998) 187-218.  
  4. 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.  
  5. Y. Achdou, P. Le Tallec, F. Valentin and O. Pironneau, Constructing wall laws with domain decomposition or asymptotic expansion techniques. Comput. Methods Appl. Mech. Engrg.151 (1998) 215-232.  
  6. 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.  
  7. A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structures. North Holland (1983).  
  8. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag (1991).  
  9. 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.  
  10. J. Cousteix, Couches Limites Laminaires. Cepadues (1989).  
  11. 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).  
  12. J. Dutton, Dynamics of atmospheric motion. Dover (1986).  
  13. L.P. Franca and F. Valentin, On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation. Comput. Methods Appl. Mech. Engrg.190 (2000) 1785-1800.  
  14. V. Girault and P.A. Raviart, Finite Element Methods for the Navier-Stokes Equations. Springer-Verlag (1986).  
  15. R. Lewandowski, Analyse mathématique et océanographie. Masson (1997).  
  16. B. Mohammadi and G. Medic, 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.  
  17. B. Mohammadi and O. Pironneau, Unsteady separated turbulent flows computation with wall-laws and k-ε model. Comput. Methods Appl. Mech. Engrg.148 (1997) 393-405.  
  18. 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.  
  19. A. Smith and D. Silvester, Implicit algorithms and their linearization for the transient incompressible Navier-Stokes equations. IMA J. Numer. Anal.17 (1997) 527-545.  
  20. R. Temam, Navier Stokes Equations. Theory and Numerical Algorithms. North-Holland, third edition (1984).  
  21. 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).  
  22. T. Yamaguchi, Computational mechanics simulation for clinical cardiovascular medicine, in ECCOMAS 2000, Barcelona (2000).  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.