Research of the Finite Difference Numerical Method Using Artificial Intelligence for Solving Problems of Incompressible Fluid Flow in a Rectangular Domain with Initial and Boundary Conditions
Abstract
This paper explores the enhancement of the finite difference method using artificial intelligence (AI) to model incompressible fluid flow within a rectangular domain. Accurate and efficient modeling of incompressible flows is crucial in hydrodynamics and aerodynamics, where traditional numerical methods like finite difference often face limitations in accuracy and computational speed, especially for complex problems with varied initial and boundary conditions. By integrating AI techniques such as neural networks and machine learning, this approach enables adaptive parameter selection, optimizing the calculation process, improving accuracy, and reducing computational demands. The combined finite difference and AI approach demonstrated significantly reduced computational complexity and improved accuracy, as verified across multiple test cases with different boundary conditions. Results indicate that AI-enhanced numerical methods improve the efficiency and reliability of solutions for complex hydrodynamic problems, offering faster, more precise modeling of fluid flow behaviors. The study highlights the potential of AI to enhance classical numerical methods, enabling the development of more accurate fluid flow models even with limited computational resources. The novelty of this work lies in the specific integration of machine learning with the finite difference method, presenting an adaptive approach that extends beyond traditional techniques. This integration opens up new possibilities for handling complex fluid dynamics scenarios, expanding the applications of numerical methods in scientific and engineering calculations.