Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes I. Abstract framework,a volume distribution of holes |
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Authors: | Grégoire Allaire |
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Institution: | (1) Commissariat à l'Energie Atomique, C.E.N. Saclay, Gif sur Yvette, France |
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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 3 and are located at the nodes of a regular mesh of size .) 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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