2020, issue 1, p. 41-52

Received 27.02.2020; Revised 02.03.2020; Accepted 10.03.2020

Published 31.03.2020; First Online 26.04.2020


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MSC 90C15, 49M27


Olga Marchenko 1,   Tetiana Samoilenko 1 *

1 V.M. Glushkov Institute of Cybernetics, Kyiv, Ukraine

* Correspondence: This email address is being protected from spambots. You need JavaScript enabled to view it.


Introduction. Calculation of dynamics of the anisothermal moisture transfer processes in axisymmetric formulation is essential in the study of wet soils condition around, for example, vertical drains, wells, piles, etc. In this paper, we formulate the initial boundary value problem for the system of moisture and heat transfer nonstationary equations. The problem is considered for isotropic medium in cylindrical coordinate system under the inhomogeneous mixed boundary conditions.

The obtained results are important for future research in cylindrical coordinates of problems that model the migration of moisture during the seasonal freezing of the soil, taking into account phase transitions from unfrozen water to ice in the entire volume of the soil mass without highlighting the crystallization front. In this case moisture exchange and heat transfer characteristics appear as functions of the total humidity. Consequently, the equation of moisture transfer is written relative to the "fictitious" moisture content. Because of the main direction of moisture migration relative to the freezing/melting front, the convective heat transfer along the vertical coordinate axis is considered to be essential that leads to sufficient coincidence with the experimental data.

The purpose of the paper is to formulate the appropriate generalized problem in the Galorkin form for the axisymmetric initial-boundary value problem. The important goal is to investigate the accuracy of the continuous in time and completely discrete approximate generalized solutions based on the finite elements method.

Results. The algorithm for constructing of approximate generalized solution of the axisymmetric initial-boundary value problem for the system of filtration and heat transfer equations is proposed. The estimates of the convergence rate for the continuous in time and discrete approximate solutions based on the finite elements method are obtained.


Keywords: moisture transfer, heat transfer, axisymmetric initial boundary value problem, generalized solution, finite elements method, Crank-Nicolson scheme.


Cite as: Marchenko O., Samoilenko T. Constructing the Approximate Solution of Axisymmetric Problem on the Dynamics of Anisothermal Moisture Transfer. Cybernetics and Computer Technologies. 2020. 1. 41–52. (in Ukrainian) https://doi.org/10.34229/2707-451X.20.1.5



           1.     Pavlov A.R., Permyakov P.P. Mathematical model and computer calculation algorithms of heat and mass transfer during soil freezing. Journal of Engineering Physics. 1983. 44 (2). P. 311316. https://doi.org/10.1007/BF00826153

           2.     Marchenko O.A., Lezhnina N.А. Appoximate solution of the problem of moisture and heat transfer in freezing soils by the finite elements method. Computer mathematics. 2002. 1. P. 24–33. (in Russian)

           3.     Marchenko O.A., Samoilenko T.A. Analyzing an approximate solution of a quasilinear parabolic-hyperbolic problem. Cybern Syst Anal. 2012. 48 (5). P. 142154. (in Russian) https://doi.org/10.1007/s10559-012-9455-2

           4.     Shastunova U. Yu. Experimental study and a mathematical model of the processes in frozen soil under a reservoir with a hot heat-transfer agent / A. A. Kislitsyn, U. Yu. Shastunova, Yu. F. Yanbikova. Journal of Engineering Physics and Thermophysics. 2018. 91 (2). Р. 507514. https://doi.org/10.1007/s10891-018-1771-6

           5.     Bogaenko V.A., Marchenko O.A., Samoilenko T.A. An analysis of numerical non-isothermal processes in a soil massif modeling. Computer mathematics. 2016. 2. P. 311. (in Russian) http://nbuv.gov.ua/UJRN/Koma_2016_2_3

           6.     Deineka V.S., Sergienko I.V., Skopetsky V.V. Mathematical models and computation methods for problems with discontinuous solutios. Kyiv: Naukova dumka, 1995. 262 p. (in Russian)

           7.     Rektorys K. Variational Methods in Mathematics, Science and Engineering.  Springer Netherlands, 1977. 571 p. https://doi.org/10.1007/978-94-011-6450-4



ISSN 2707-451X (Online)

ISSN 2707-4501 (Print)

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