Homogenization of the Navier-Stokes Equations in Open Sets Perforated with Tiny Holes I. Abstract Framework, a Volume Distribution of Holes
نویسنده
چکیده
This paper treats the homogeniza t ion of the Stokes or Navier-Stokes equat ions with a Dirichlet bounda ry condi t ion in a domain conta in ing many t iny solid obstacles, periodically dis tr ibuted in each direction of the axes. (For example, in the three-dimensional case, the obstacles have a size of e a and are located at the nodes of a regular mesh of size e.) A suitable extension of the pressure is used to prove the convergence of the homogeniza t ion process to a Br inkmantype law (in which a l inear zero-order term for the velocity is added to a Stokes or Navier-Stokes equation).
منابع مشابه
Homogenization of the Navier-Stokes Equations in Open Sets Perforated with Tiny Holes II: Non-Critical Sizes of the Holes for a Volume Distribution and a Surface Distribution of Holes
This paper is devoted to the homogenizat ion of the Stokes or Navier-Stokes equations with a Dirichlet boundary condit ion in a domain containing many tiny solid obstacles, periodically distributed in each direction of the axes. For obstacles of critical size it was established in Part I that the limit problem is described by a law of Brinkman type. Here we prove that for smaller obstacles, the...
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