C&SA | Contents

Volume 59 >>> № 5 SEPTEMBER — OCTOBER 2023

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UDC 517.9, 517.6

D.A. Klyushin¹, S.I. Lyashko², N.I. Lyashko³, A.A. Tymoshenko⁴

¹ Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

dokmed5@.gmailcom

² Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

lyashko.serg@gmail.com

³ Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Lyashko@nas.gov.ua

⁴ Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

inna-andry@ukr.net

OPTIMAL LUMPED CONTROL OF WATER TRANSPORT IN POROUS MEDIA

Abstract. An algorithm for finding the optimal source power for the two-dimensional quasi-linear Richards equation for a rectangular region is proposed. The Kirchhoff transformation with scaling of coordinates and powers of buried sources is used, which allows formulating a dimensionless problem. The existence of the solution for the problem of optimizing moisture transfer in an unsaturated porous medium is substantiated. The task of this study is to find the power of sources buried in a porous medium — such that at the final moment of time the distribution of humidity will be close to the given indicators or the objective function. The numerical solution leads to an approximation of the optimal мalues of the sources.

Keywords: Richards equation, control, optimization, porous medium, moisture transfer.

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