Archive for Rational Mechanics and Analysis

, Volume 113, Issue 3, pp 209–259 | Cite as

Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes I. Abstract framework, a volume distribution of holes

  • Grégoire Allaire
Article

Abstract

This paper treats the homogenization of the Stokes or Navier-Stokes equations with a Dirichlet boundary condition in a domain containing many tiny solid obstacles, periodically distributed in each direction of the axes. (For example, in the three-dimensional case, the obstacles have a size of ε3 and are located at the nodes of a regular mesh of size ε.) A suitable extension of the pressure is used to prove the convergence of the homogenization process to a Brinkman-type law (in which a linear zero-order term for the velocity is added to a Stokes or Navier-Stokes equation).

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Grégoire Allaire
    • 1
  1. 1.Commissariat à l'Energie AtomiqueC.E.N. SaclayGif sur YvetteFrance

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