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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. (English) Zbl 0724.76021

This article is a continuation of Part I on the homogenization of the Stokes (Navier-Stokes) equations [see the foregoing entry (Zbl 0724.76020)]. The convergence of the problem to the Stokes and the Darcy laws, depending on the hole size being smaller and larger, respectively, than the critical size as defined in the first part, is established. Moreover, a different geometric distribution of holes in considered on a hyperplane H which intersects the fluid medium, with the typical hole size \(\epsilon^ 2\) for \(N=2\) and \(e^{-1/\epsilon}\) for \(N=3\). The method developed in first part has been used to derive a weaker estimate satisfied by the pressure in this case. The results also provide an effective method for computing viscous fluid flows through porous walls, or mixing grids.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations

Citations:

Zbl 0724.76020
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References:

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