Abstract
<jats:p>Предложена математическая модель формирования теплового режима в промерзающем/протаивающем грунте, учитывающая изменяющиеся фильтрационные свойства и возможность обмена массой между фазами во всем слое грунта. Разработан численный алгоритм решения одномерной задачи фильтрации воды и воздуха в грунте с учетом фазового перехода лед – вода. Проведена верификация математической модели на экспериментальных данных из литературных источников. Численными экспериментами показано формирование слоя грунта с меньшей проницаемостью, влияющего на впитывающую способность грунта. Разработанная математическая модель может быть использована при разработке методик расчетов и прогнозов гидрографов весеннего половодья.</jats:p> <jats:p>Objective. The objective of this study is to examine the mathematical model of ground freezing and thawing, incorporating phase transitions and capillary forces. This will involve developing an algorithm for numerical solution of a one-dimensional problem, conducting numerical experiments for ascertain changes in soil porosity and absorption capacity, and determining the area of active phase transition. Methods. In order to approximate the nonlinear equations numerically, a difference scheme of first-order accuracy in both spatial coordinates and time was employed, with a directed difference applied to the convective component and the Runge – Kutta method used for the second-order accuracy. The mesh convergence was verified by means of a series of computational experiments on sequences of chopped meshes. Results. The mathematical model of thermal regime formation in freezing/thawing soil is propo- sed, which takes into account changing filtration properties and the possibility of mass exchange between phases in the entire soil layer. A numerical algorithm for solving the one-dimensional problem of water and air filtration in the ground, taking into account the ice-water phase transition, has been developed. The results of numerical experiments demonstrate the formation of a layer with significantly lower porosity and, consequently, permeability. The mathematical model allows estimating of the volume of surface and ground runoff during spring snowmelt and taking into account the changing permeability of the upper soil layers. Conclusions. The results of numerical experiments demonstrate the formation of a soil layer with reduced permeability, which impacts the soil’s absorption capacity. The developed mathematical model can be employed in the development of methodologies for calculating and forecasting the hydrograph of spring floods.</jats:p>