The problem of a two-dimensional creeping flow of a viscous incompressible liquid in a flat channel partially filled with a model fibrous porous medium that is represented by a regular system of square cylinders located across the flow is analyzed. Two forms of flows are considered: a shear flow due to the motion of the upper wall of the channel and a gradient flow due to the presence of a pressure drop along the channel. The hydrodynamic microscopic fields of velocity are found numerically. The macroparameters such as the filtration velocity, the permeability of a system of cylinders, the flow rate of the liquid through the channel, tangential stresses on the upper wall of the channel and the porous boundary, and a slip coefficient are obtained as a result of averaging. Using these parameters in the Saffman slip boundary condition it is possible to complete the settings of the macroscopic boundary value problems for the fluid flow near the porous interface.
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