• G. V. Sandrakov Faculty of Computer Science and Cybernetics, Taras Shevchenko Kiev National University, Kiev, Ukraine
Keywords: multiphase diffusion, filtration processes, porous media, modeling, initial-boundary value problems, homogenized models


Non-stationary processes of mutual diffusion for multiphase flows of immiscible liquids in porous media with a periodic structure are considered. The mathematical model for such processes is initial-boundary diffusion problem for media formed by a large number of «blocks» having low permeability and separated by a connected system of «cracks» with high permeability. Taking into account such a structure of porous media during modeling leads to the dependence of the equations of the problem on two small parameters of the porous medium microscale and the block permeability. Homogenized initial-boundary value problems will be obtained. Solutions of the problems are approximated for the solutions of the initial-boundary value problem under consideration.


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