On the Homogenization of the Stokes Problem in a Perforated Domain

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 a N tends to zero. Under the assumption th...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis Vol. 230; no. 3; pp. 1179 - 1228
Main Author: Hillairet, M.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2018
Springer Nature B.V
Springer Verlag
Subjects:
Analysis of PDEs
Classical Mechanics
Complex Systems
Fluid- and Aerodynamics
Mathematical and Computational Physics
Mathematics
Physics
Physics and Astronomy
Theoretical
ISSN:0003-9527, 1432-0673
Online Access:Get full text
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Summary: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 a N tends to zero. Under the assumption that a N scales like a/N and that there is no concentration in the distribution of holes, we prove that the solution is well approximated asymptotically by solving a Stokes–Brinkman problem.
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ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-018-1268-7