Mathematics

A coupled Darcy-Stokes system modeling flow in porous media with a flat fracture will be presented. Boundary and interface conditions are given as well as an appropriate scaling of the system in order to perform its asymptotic analysis when the thickness of the fracture tends to zero. The main techniques of the asymptotic analysis will be presented together with a Darcy-Brinkman coupled system as a limiting problem. Finally a quick overview on the strategies used in generalizing the geometry of the interface and the fracture will be presented.