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Darcy's laws for non‐stationary viscous fluid flow in a thin porous medium
Author(s) -
Anguiano Maria
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4204
Subject(s) - porous medium , darcy's law , limit (mathematics) , mathematics , stokes flow , zero (linguistics) , viscous liquid , flow (mathematics) , porosity , mechanics , law , mathematical analysis , physics , geometry , geotechnical engineering , geology , linguistics , philosophy , political science
We consider a non‐stationary Stokes system in a thin porous medium Ω ϵ of thickness ϵ which is perforated by periodically solid cylinders of size a ϵ . We are interested here to give the limit behavior when ϵ goes to zero. To do so, we apply an adaptation of the unfolding method. Time‐dependent Darcy's laws are rigorously derived from this model depending on the comparison between a ϵ and ϵ . Copyright © 2016 John Wiley & Sons, Ltd.