A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series S Année : 2014

A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium

Résumé

We present modeling of an incompressible viscous flow through a fracture adjacent to a porous medium. We consider a fast stationary flow, predominantly tangential to the porous medium. Slow flow in such setting can be described by the Beavers-Joseph-Saffman slip. For fast flows, a nonlinear filtration law in the porous medium and a non- linear interface law are expected. In this paper we rigorously derive a quadratic effective slip interface law which holds for a range of Reynolds numbers and fracture widths. The porous medium flow is described by the Darcys law. The result shows that the interface slip law can be nonlinear, independently of the regime for the bulk flow. Since most of the interface and boundary slip laws are obtained via upscaling of complex systems, the result indicates that studying the inviscid limits for the Navier-Stokes equations with linear slip law at the boundary should be rethought.

Dates et versions

hal-00863443 , version 1 (18-09-2013)

Identifiants

Citer

Anna Marciniak-Czochra, Andro Mikelic. A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium. Discrete and Continuous Dynamical Systems - Series S, 2014, 7, pp.1065-1077. ⟨10.3934/dcdss.2014.7.1065⟩. ⟨hal-00863443⟩
146 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More