Derivation of a quasi‐stationary coupled Darcy–Reynolds equation for incompressible viscous fluid flow through a thin porous medium with a fissure | Zendy

Anguiano María | Zendy

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Derivation of a quasi‐stationary coupled Darcy–Reynolds equation for incompressible viscous fluid flow through a thin porous medium with a fissure

Author(s) -

Anguiano María

Publication year - 2017

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.4341

Subject(s) - porous medium , reynolds number , darcy's law , mathematics , fissure , mechanics , compressibility , limit (mathematics) , stokes flow , viscous liquid , flow (mathematics) , reynolds equation , mathematical analysis , geometry , porosity , physics , turbulence , materials science , geotechnical engineering , geology , composite material

We consider a non‐stationary Stokes system in a thin porous medium of thickness ε that is perforated by periodically distributed solid cylinders of size ε , and containing a fissure of width η ε . Passing to the limit when ε goes to zero, we find a critical sizeη ε ≈ ε2 3in which the flow is described by a 2D quasi‐stationary Darcy law coupled with a 1D quasi‐stationary Reynolds problem. Copyright © 2017 John Wiley & Sons, Ltd.

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