High-Order Dynamic Integration Method (HODIM) for Modeling Turbulent Fluid Dynamics

Abstract

This research explores the development and application of the High-Order Dynamic Integration Method for solving integro-differential equations, with a specific focus on turbulent fluid dynamics. Traditional numerical methods, such as the Finite Difference Method and the Finite Volume Method, have been widely employed in fluid dynamics but struggle to accurately capture the complexities of turbulence, particularly in high Reynolds number regimes. These methods often require significant computational resources and are prone to errors in nonlinear dynamic systems. The High-Order Dynamic Integration Method addresses these challenges by integrating higher-order interpolation techniques with dynamic adaptation strategies, significantly enhancing accuracy and computational efficiency. Through rigorous numerical analysis, this method demonstrates superior performance over the Finite Difference Method and the Finite Volume Method in handling the nonlinear behaviors characteristic of turbulent flows. Furthermore, the High-Order Dynamic Integration Method achieves this without a substantial increase in computational cost, making it a highly efficient tool for simulations in computational fluid dynamics. The research validates the capabilities of the High-Order Dynamic Integration Method through a series of benchmark tests and case studies. Results indicate a marked improvement in both accuracy and stability, particularly in simulations of high-Reynolds-number flows, where traditional methods often falter. This innovative approach offers a robust and efficient alternative for solving complex fluid dynamics problems, contributing to advances in the field of numerical methods and computational fluid dynamics.