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International Theoretical Science Journal
Volume 62 >>> № 1 JANUARY — FEBRUARY 2026
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DOI 10.34229/KCA2522-9664.26.1.7
UDC 519.6

D.A. Klyushin
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
 dmytroklyushin@knu.ua

V.A. Kolesnykov
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
 valerii.kolesnykov@knu.ua

S.I. Lyashko
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
 sergiylyashko@gmail.com


MASS TRANSFER PROBLEM WITH SATURATION LIMIT
AND FLOW RESTRICTIONS IN GRAPH STRUCTURED
POROUS MEDIA

Abstract. The task of this study is to derive equations describing the mass transfer process in a porous medium on a graph with additional constraints on the mass flow rate on some edges, which can be interpreted as a model for an irrigation system with taps on some pipes. The task is also to construct a numerical method for approximating the solution of the problem, which is based on numerical methods for solving one-dimensional mass transfer problems and takes into account the flow rate constraints. The paper considers the problem of mass transfer in a porous medium on a graph with additional constraints on the flow rate on the edges. The existence of a solution to the problem is substantiated for the case of an unsaturated medium as the initial condition and monotonically increasing boundary conditions. Computational experiments were conducted.

Keywords: Richards–Klute equation, mathematical modeling, mass transfer, graphs.


full text

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