Modeling of Transfers at a Fluid-Porous Interface: A Multi-Scale Approach

Abstract

Free flows above porous medium are present in many industrial or environmental applications. To study such problems, a common approach consists of coupling a free fluid model with a porous model, the transfers that occur at the fluid-porous interface being modeled through appropriate boundary conditions. However, the determination of these boundary conditions is not trivial and remains an important issue for the study of practical applications. Here, we present a multi-scale method that allows to determine the form of the boundary conditions and the value of the jump parameters that appear in the expression of these boundary conditions. This theoretical approach allows to analyze the physical nature of the jump coefficients, to understand the importance of the interface location and to determine whether these jump coefficients are intrinsic parameters or not.

Keywords: Darcy-Brinkman model, diffusive mass transfer, fluid-porous interface, Forchheimer model, interface location, intrinsic parameters, jump parameters, Kelvin-Helmholtz instability, multi-scale method, Stokes model, transition region, up-scaling tools.