Upstream boundary conditions for flows in porous channels

摘要

The apstream velocity profile for the Darcy-Forchheimer-Brinkman and Darcy-Lapwood-Forchheimer-Brinkman models of flow in porous channels is determined analytically as a function of the Reynolds number, permeability of the medium, and drag coefficient. It is shown that this profile is governed by the Korteweg-de Vries equation in a frame moving at constant speed and given as a Jacobi elliptic function on account of the no-slip boundary conditions at the solid walls.