Ключевое слово: «finite element method»

This paper examines fluid flow and transport modeling in porous media, focusing on the influence of Robin boundary conditions. A mixed finite element method is employed to approximate the Stokes equation governing fluid motion. Additionally, the transport equation for substance concentration is analyzed, with solutions obtained using the Streamline Upwind/Petrov-Galerkin (SUPG) method for different diffusion coefficients. The sequential solution approach integrates fluid dynamics and transport phenomena to enhance accuracy. Numerical results are presented for a three-dimensional model, highlighting the interplay between flow, transport, and boundary conditions. This study provides insights into the behavior of fluids in porous structures, aiding ap-plications in fields like hydrology, petroleum engineering, and environmental science.

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.