A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium
Anna Marciniak‐Czochra, Andro Mikelić · Discrete and Continuous Dynamical Systems - S · 2014
We present modeling of an incompressible viscous flow through a fractureadjacent to a porous medium. A fast stationary flow,predominantly tangential to the porous medium is considered. Slow flow in such setting canbe described by the Beavers-Joseph-Saffman slip. For fast flows, a nonlinearfiltration law in the porous medium and a non- linear interface law areexpected. In this paper we rigorously derive a quadratic effective slipinterface law which holds for a range of Reynolds numbers and fracturewidths. The porous medium flow is described by the Darcy law. The resultshows that the interface slip law can be nonlinear, independently of theregime for the bulk flow. Since most of the interface and boundary slip lawsare obtained via upscaling of complex systems, the result indicates thatstudying the inviscid limits for the Navier-Stokes equations with linear slip law at the boundary should be rethought.