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

María Anguiano; Francisco Javier Suárez-Grau; María Anguiano; Francisco Javier Suárez-Grau

doi:10.3934/nhm.2019012

Networks and Heterogeneous Media

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
,},
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

Received: 01 April 2018 Revised: 01 September 2018
Primary: 76A20, 76M50, 35B27; Secondary: 76S05

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.
- Homogenization,
- Stokes system,
- Darcy's law,
- thin porous medium,
- non-homogeneous slip boundary condition
Citation: María Anguiano, Francisco Javier Suárez-Grau. Newtonian fluid flow in a thin porous medium with non-homogeneous slip boundary conditions[J]. Networks and Heterogeneous Media, 2019, 14(2): 289-316. doi: 10.3934/nhm.2019012

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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.

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