Derivation of a coupled Darcy–Reynolds equation for a fluid flow in a thin porous medium including a fissure

  • María AnguianoEmail author
  • Francisco Javier Suárez-Grau


We study the asymptotic behavior of a fluid flow in a thin porous medium of thickness \(\varepsilon \), which is characteristic size of the pores \(\varepsilon \) and contains a fissure of width \(\eta _\varepsilon \). We consider the limit when the size of the pores tends to zero, and we find a critical size \(\eta _\varepsilon \approx \varepsilon ^{2\over 3}\) in which the flow is described by a 2D Darcy law coupled with a 1D Reynolds problem. We also discuss the other cases.


Stokes equation Darcy’s law Reynolds equation Thin porous medium Fissure 

Mathematics Subject Classification

75A05 76A20 76M50 35B27 


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© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Departamento de Análisis Matemático, Facultad de MatemáticasUniversidad de SevillaSevillaSpain
  2. 2.Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de MatemáticasUniversidad de SevillaSevillaSpain

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