A nonlinear asymptotic model for the inertial flow at a fluid-porous interface

Abstract

An original nonlinear multi-dimensional model for the inertial fluid flow through a fluid-porous interface is derived by asymptotic theory for arbitrary flow directions. The interfacial region between the pure fluid and the homogeneous porous region is viewed as a thin transition porous layer characterized by smoothly evolving heterogeneities. The asymptotic analysis applied to the homogenized Navier-Stokes equations in this thin heterogeneous porous layer leads to nonlinear momentum jump conditions at the equivalent dividing interface. These jump conditions involve slip and friction coefficients whose dependence on porosity are analyzed. Moreover, we show that the resulting Navier-Stokes/Darcy-Forchheimer macroscale coupled model is globally dissipative in the porosity range 0<ϕp≤0.95,which also contributes to its physical relevance. To our knowledge, this innovative asymptotic model is the first nonlinear multi-dimensional model proposed in the literature for the inertial flow with arbitrary flow directions at a permeable interface. Besides, it clearly opens new perspectives to study turbulent flows at the fluid-porous interface.