NUMERICAL METHODS FOR APPROXIMATE CALCULATION OF TURBULENT FLOWS IN ENGINEERING SYSTEMS AND THEIR CONVERGENCE ANALYSIS.

This paper investigates the mathematical modeling of turbulent flows within engineering systems. The research focuses on numerical algorithms for solving the non-linear Navier-Stokes equations, specifically utilizing the SIMPLE algorithm coupled with the k-epsilon turbulence model. The study performs a rigorous mathematical analysis of the impact of mesh refinement on computational accuracy and the stability of the convergence process. The results demonstrate that the proposed numerical scheme allows for high-fidelity prediction of hydrodynamic processes and the optimization of energy dissipation in engineering devices. The findings provide a robust computational framework for hydraulic infrastructure design.