Advertisement

Convection of Microstructures by Incompressible and Slightly Compressible Flows

  • T. Chacon
  • O. Pironneau
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 2)

Abstract

In this paper we wish to extend the work of McLaughlin-Papanicolaou-Pironneau [11] to compressible flows. Thus we shall first summarize the results for imcompressible fluids then present the current state of numerical simulation of these problems and finally make some preliminary statements on the extension to compressible flows and the possible applications to turbulence and acoustics.

Keywords

Turbulence Modeling Compressible Flow Compressible Fluid Homogeneous Turbulence Stochastic Nonlinear System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    C. Begue: These de 3eme cycle. Universite Paris 6 (1984).Google Scholar
  2. [2]
    A. Bensoussan, J.L. Lions, 6. Papanicolaou: Asymptotic methods for periodic structures. North Holland (1978).Google Scholar
  3. [3]
    T. Chacon: These de 3eme cycle. Universite Paris 6 (1985).Google Scholar
  4. [4]
    T. Chacon, O. Pironneau: On the mathematical foundations of the k-ε turbulence model. (To appear)Google Scholar
  5. [5]
    R. DiPerna, A. Majda: to appear (see also Majda-Hunter-Rosales: Resonantly interacting weakly nonlinear hyperbolic waves. Studies in Applied Mathematics. Elsevier (1984)).Google Scholar
  6. [6]
    U. Frisch, O. Thual, Z.S. She: Homogenization and visco-elasticity of turbulence Proc. workshop on Turbulence (Nice 1984) To appear in Springer Lecture notes in Physics (Frisch-Keller-Papanicolaou-Pironneau ed).Google Scholar
  7. [7]
    J. Hunter, J.B. Keller: Weakly nonlinear high frequency waves. Comm Pure Appl. Math, 36(5): 547–569, 1983.MathSciNetADSMATHCrossRefGoogle Scholar
  8. [8]
    L. Landau, E. Lifschitz: Mecanique des fluides. Moscou (1962) MIR.Google Scholar
  9. [9]
    B. Launder, D. Spalding: Mathematical models of Turbulence. Academic press (1972).MATHGoogle Scholar
  10. [10]
    J. Mathieu: Cours de Turbulence Ecole d’ete EDF-CEA 1982.Google Scholar
  11. [11]
    D. McLaughlin, kG. Papanicoulaou, O. Pironneau: Convection of microstructures. Siam Numer Anal (to appear).Google Scholar
  12. [12]
    A. Monin, A. Yaglom: Statistical Fluid Mechanics of Turbulence. MIT (1975).Google Scholar
  13. [13]
    S. Orszag: Lecture on statistical theory of turbulence. (Ecole d’ete des Houches, 1973). Gordon Breach, London 1977.Google Scholar
  14. [14]
    G. Papanicolaou, O. Pironneau: On the asymptotic behavior of motion in random flow. In Stochastic Nonlinear Systems, Arnold-Lefever eds. Springer (1981).Google Scholar
  15. [15]
    A. Patera, S. Orszag: 3-D instability in plane channel flow at subcritical Reynolds number. In Numerical and Physical Aspect of aerodynamic flows. (Long Beach 1981) 69–86 Springer (1982).Google Scholar
  16. [16]
    P. Perrier, O. Pironneau. Subgrid turbulence modeling by homogenization. Math Modeling, Vol. 2, 295–317 (1981).MathSciNetMATHCrossRefGoogle Scholar
  17. [17]
    W.C. Reynolds: Computation of turbulent flows. Annual Rev. Fluid Mech. 8, 183–208 (1976).ADSCrossRefGoogle Scholar
  18. [18]
    P. Saffman: A model for inhomogeneous turbulent flow. Proc. Roy. Soc. London A317 (1970) 417–433.ADSGoogle Scholar
  19. [19]
    U. Shumann: Subgrid scale model for finite difference simulations of turbulent flows in plane channel and annuli. J. Comp. Phys. 18, 376–404 (1975).ADSCrossRefGoogle Scholar
  20. [20]
    J. Smagorinsky: Mon. Weather Rev. 91, 99–164.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • T. Chacon
    • 1
  • O. Pironneau
    • 2
  1. 1.INRIALe ChesnayFrance
  2. 2.INRIA and University of Paris-13France

Personalised recommendations