Development of a Numerical Algorithm and Model Based on the Finite Element Method for the Study of Flows in Channels

This paper presents the development of a numerical algorithm and model based on the Finite Element Method (FEM) for studying fluid flows in channels. The study focuses on solving the Navier-Stokes equations using FEM, which allows for flexible handling of complex geometries and boundary conditions. The algorithm discretizes the channel into finite elements, applies variational principles, and incorporates iterative solvers to address the non-linear nature of the flow equations. The developed model is validated by comparing the results with analytical solutions and experimental data. The model provides accurate predictions of flow behavior in various channel configurations, making it a valuable tool for simulating real-world fluid dynamics problems in engineering applications. This approach offers insight into optimizing channel designs, improving flow efficiency, and applying adaptive mesh refinement for higher accuracy in critical regions.