|Title:|| A multiscale Darcy-Brinkman model for fluid flow in fractured porous media|
|Date:|| Thursday 4th November 2010|
|Author(s) :|| Lesinigo, Matteo; D'angelo, Carlo; Quarteroni, Alfio|
|Abstract:|| The aim of this work is to present a reduced mathematical model for describing fluid flow in porous media featuring open channels or fractures.
The Darcy s law is assumed in the porous domain while the Stokes-Brinkman equations are considered in the fractures. We address the case of fractures whose thickness is very small compared to the characteristic diameter of the
computational domain, and describe the fracture as if it were an interface between porous regions. We derive the corresponding interface model governing the fluid flow in the fracture and in the porous media, and establish the
well-posedness of the coupled problem. Further, we introduce a finite element scheme for the approximation of the coupled problem, and discuss solution strategies. We conclude by showing the numerical results related to several test cases and compare the accuracy of the reduced model compared with the non-reduced one.|