Том: 2919 CCIS , Год издания: 2026

We present numerical procedure for mathematical simulation the seasonal change in temperature of frozen rocks during natural and constant temperature influence from a drilled well. We apply an effective model of the upper layer of frozen rocks to study the influence of seasonal changes in the temperature background during the annual period, taking into account the borehole surface temperature effect on the degradation process of permafrost rocks. These rocks are characterized by high intensity of moisture phase transitions at positive temperatures. Two mathematical models are used to simulate the above processes. The first model is based on the Stefan problem with explicit tracking of the phase transition front in a medium with inclusions having phase-changing properties. The second mathematical model is based on the heat conduction problem with phase transformations in enthalpy formulation. To reconcile the two mathematical models, we require continuity of the temperature and the normal component of the heat flux at the interface of the two domains. This approach allows us to take into account the natural multiscale nature of the object under study. For spatial discretization of mathematical models, the computational scheme of the discontinuous Galerkin method is used. The Runge-Kutta scheme is used for time discretization. Due to the block structure of the resulting system of algebraic equations, parallel realization of the problem solver is possible. To study the structural changes of frozen soil during thawing, the problem of numerical simulation of the thermoelastic deformation process is posed. The discretization of mathematical model is performed using the heterogeneous multiscale finite element method. We analyzed the results of computational experiments. We found that the borehole has a significant effect on the process of soil thawing during periods of sub-zero temperatures. In periods of positive day and night temperatures, phase transitions depend less on the borehole temperature. During the transition periods from positive to negative temperatures, two fronts of phase transitions are observed: from the day surface and from the deep-frozen ground layers. Thus, there are stress states that can lead to changes in soil structure in permafrost areas.