Derivation of a quasi-stationary coupled Darcy-Reynolds equation for incompressible viscous fluid flow through a thin porous medium with a fissure
María Anguiano · Mathematical Methods in the Applied Sciences · 2017
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 ηε. Passing to the limit when ε goes to zero, we find a critical size in 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.