Mathematical Description of Fluid Flow in a Porous Medium

A mathematical model and a numerical method for the study are presented flows in the combined region. This region includes a porous medium, through the pores of which the liquid moves, and a zone without a porous framework (free zone). The flow is modeled with a single equation for the weight area, based on an interpenetrating heterogeneous model. In the one-dimensional case, an analytical solution is obtained. This solution is compared with the solution obtained by the moving node method. The analysis of experimental data with the Brinkman layer has been carried out. A numerical solution is obtained for a two-dimensional problem with a partially filled porous medium.