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Pré-Publication, Document De Travail Année : 2016

On the homogenization of the Stokes problem in a perforated domain

Matthieu Hillairet

Résumé

We consider the Stokes equations on a bounded perforated domain completed with non-zero constant boundary conditions on the holes. We investigate configurations for which the holes are identical spheres and their number N goes to infinity while their radius 1/N tends to zero. We prove that, under the assumption that there is no concentration in the distribution of holes, the solution is well approximated asymptotically by solving a Stokes-Brinkman problem.
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Dates et versions

hal-01302560 , version 1 (14-04-2016)
hal-01302560 , version 2 (05-09-2016)
hal-01302560 , version 3 (11-05-2017)
hal-01302560 , version 4 (31-05-2018)

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Matthieu Hillairet. On the homogenization of the Stokes problem in a perforated domain. 2016. ⟨hal-01302560v3⟩
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