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International Theoretical Science Journal
Volume 59 >>> № 2 MARCH — APRIL 2023
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UDC 517.9, 519.6
G.V. Sandrakov1, S.I. Lyashko2, V.V. Semenov3


1 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

 gsandrako@gmail.com

2 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

 lyashko.serg@gmail.com

3 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

 semenov.volodya@gmail.com

SIMULATION OF FILTRATION PROCESSES FOR INHOMOGENEOUS MEDIA
AND HOMOGENIZATION

Abstract. The investigation of the dynamic processes of filtration in porous media is essential when planning the use of underground resources and simulation of systems in ecology. Porous periodic media, formed by a large number of “blocks” with low permeability, and separated by a connected system of “faults” with high permeability, will be considered here. Taking into account the structure of such media in modeling leads to the dependence of the filtration equations and their coefficients on a small parameter characterizing the microscale of the porous medium and the permeability of the blocks. Thus, initial boundary value problems for nonstationary equations of filtration in such porous media are considered. Homogenized problems (whose solutions determine approximate asymptotics for solutions of the original problems) are presented. The homogenized problems have the form of initial boundary value problems for integro-differential equations in convolutions. Estimates for the accuracy of the asymptotics and relevant convergence theorem are discussed. Statements about the solvability and regularity for the problems and the homogenized problems are proved. The statements are optimal and do not depend on the parameters.

Keywords: homogenized problems, parabolic problems, approximate asymptotics, solvability, a priori estimates, Laplace transforms.


full text

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