Two-dimensional flows in finite-width channels partially filled with porous medium

A stationary two-dimensional liquid flow in a channel partially filled with a porous non-deformable homogeneous medium is investigated numerically based on the proposed mathematical model. The homogeneous liquid is bounded by a solid or free rigid boundary, while the channel bottom is solid. The model is constructed based on the Berman transformation. The free flow is described by the Navier-Stokes equations and the filtration flow is described by the Darcy-Brinkman model. The interfacial boundary conditions include the velocity continuity and the balance of tangential and normal viscous stresses; the tangential stresses may have a discontinuity at the boundary. The numerical solution is found by the finite-difference relaxation method. It has been shown that the flow of the liquid into porous medium takes place for a wide parameter range. However in most cases, the transversal velocity is about 10-7 of the maximum longitudinal velocity. The dependence of the transversal velocity on the permeability of porous medium and its thickness is examined...