Newtonian fluid flow in a thin porous medium with non-homogeneous slip boundary conditions

María Anguiano; Francisco Javier Suárez-Grau

doi:10.3934/nhm.2019012

Article Contents

2019, Volume 14, Issue 2: 289-316. Doi: 10.3934/nhm.2019012

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Newtonian fluid flow in a thin porous medium with non-homogeneous slip boundary conditions

María Anguiano^1, and
Francisco Javier Suárez-Grau^2, ,

1.
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, P. O. Box 1160, 41080-Sevilla, Spain
2.
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, 41012-Sevilla, Spain

^* Corresponding author: Francisco Javier Suárez-Grau
^* Corresponding author: Francisco Javier Suárez-Grau

Received: April 2018

Revised: September 2018

Published: April 2019

María Anguiano is supported by Junta de Andalucía (Spain), Proyecto de Excelencia P12-FQM-2466. Francisco Javier Suárez-Grau is supported by Ministerio de Economía y Competitividad (Spain), Proyecto Excelencia MTM2014-53309-P.

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Abstract

We consider the Stokes system in a thin porous medium $ \Omega_\varepsilon $ of thickness $ \varepsilon $ which is perforated by periodically distributed solid cylinders of size $ \varepsilon $. On the boundary of the cylinders we prescribe non-homogeneous slip boundary conditions depending on a parameter $ \gamma $. The aim is to give the asymptotic behavior of the velocity and the pressure of the fluid as $ \varepsilon $ goes to zero. Using an adaptation of the unfolding method, we give, following the values of $ \gamma $, different limit systems.

Keywords:

Homogenization,
Stokes system,
Darcy's law,
thin porous medium,
non-homogeneous slip boundary condition.

Mathematics Subject Classification: Primary: 76A20, 76M50, 35B27; Secondary: 76S05.

Citation:

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Figure 1. Views of a periodic cell in 2D (left) and 3D (right)

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Figure 2. View of $ \omega_\varepsilon $

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Figure 3. Views of the domain $ \Omega_\varepsilon $ (left) and $ \Lambda_\varepsilon $ (right)

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