Ключевое слово: «numerical modeling»

The paper considers numerical modeling of thermoelasticity problems in heterogeneous areas. A modeling methodology based on the finite element method has been developed and implemented. The main problems of thermal conductivity, elasticity and thermoelasticity in homogeneous areas are investigated to verify the correctness of the methods. The analysis of the effect of the discretization of the calculated grid on the accuracy of solutions was carried out, which made it possible to determine the optimal grid parameters. Next, thermoelasticity modeling was performed in inhomogeneous areas, including materials with variable physical characteristics. The results of numerical experiments confirmed the effectiveness of the proposed methods, and also demonstrated the significant influence of heterogeneity on the temperature and mechanical charac-teristics of the system. The data obtained can be used to design structures subject to thermoelastic deformations in various engineering applications.

Understanding heat and mass transfer processes, especially those involving phase transitions, is fundamental for engineering applications in permafrost regions. These processes significantly influence the stability and design of structures, making accurate modeling a critical challenge. This research presents a robust mathematical model coupled with a numerical method to analyze the interplay of heat transfer, fluid motion, and phase transitions. By employing advanced finite element methods, the study provides a reliable tool for simulating scenarios that mimic real-world conditions in frozen soils. The simulations, performed across various geometric configurations, demonstrate the model's effectiveness in capturing complex dynamic phenomena, such as the movement of fluids and temperature evolution during phase transitions. These insights are particu-larly valuable for designing resilient infrastructure, such as pipelines and foundations, in harsh, extreme climates where permafrost stability is a critical concern. The study thus bridges the gap between theoretical modeling and practical engineering solutions.

The article considers, numerically implements, and thoroughly analyzes various mathematical models that describe the complex dynamics of the spread of infectious diseases. This analysis is conducted using the specific example of a large and devastating outbreak of the disease caused by the Ebola virus in Sierra Leone during the year 2014. By examining this particular case, the article aims to highlight the effectiveness of different modeling approaches in understanding how infectious diseases propagate through populations, the factors influencing transmission rates, and the potential impact of public health interventions. Furthermore, it discusses the implications of these models for future outbreak prediction and control strategies.