Кібернетика та комп'ютерні технології (Mar 2020)

Construction of the Approximate Solution of Axisymmetric Problem of the Dynamics of Non-Isothermal Moisture Transfer

  • Olga Marchenko,
  • Tetiana Samoilenko

DOI
https://doi.org/10.34229/2707-451X.20.1.5
Journal volume & issue
no. 1
pp. 41 – 52

Abstract

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Introduction. The calculation of the dynamics of non-isothermal moisture transfer processes in an 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 for isotropic medium in cylindrical coordinate sys-tem with the inhomogeneous mixed boundary conditions. The results obtained are also important for further investigation in cylindrical coordinates of problems modeling the migration of moisture during the seasonal soil freezing-throught in the case, when the phase transitions from unfrozen water to ice are taken into account in the whole volume of the soil mass without separation of the crystallization front. In this case moisture exchange and heat transfer characteristics are functions of total humidity, and the equation of moisture transfer is written relative to the "fictitious" moisture content. Taking into account the directions of migration of moisture relative to the freezing/melting front, convective heat transfer along the vertical coordinate axis is essential and allows sufficient coincidence with the experimental data. The purpose of the paper is to formulate the appropriate generalized problem in the form of Galorkin for the axisymmetric initial-boundary value problem and investigate the accuracy of the continuous in time and completely discrete approximated generalized solutions, based on the finite elements method. Results. The algorithm for constructing of the approximate generalized solution of the axisymmetric initial-boundary value problem for the system of filtration and heat transfer equations which simulates non-stationary non-isothermal processes in water-saturated soils has been proposed. The estimates of the rate of convergence for the continuous in time and discrete approximate solutions based on the finite elements method have been obtained.

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