AI-Driven Adaptive Numerical Schemes for High-Precision Computational Fluid Dynamics

Abstract

Computational Fluid Dynamics High-fidelity simulations can demand exceptionally small spatial and temporal resolutions, making them highly computationally expensive. The classical numerical methods are based on the use of fixed discretization methods that are not very efficient in providing accuracy to a flow problem involving multi-scales. To overcome these drawbacks, this paper suggests the adaptive numerical scheme, which is AI-driven, and dynamically optimises computational resources by observing the characteristics of flows in the learned features and error distributions. The suggested framework incorporates a machine learning model and a standard CFD solver to steer adaptive refinements in meshes and updates to the solutions in real time. The approach uses predictive capabilities to determine areas that need greater resolution and eliminate unnecessary computations in smooth flow regions. Standard error measures are strictly assessed, such as L2 norm and L∞ norm, to provide both average and worst-case measurements of error. Simulations at the benchmark prove that the proposed method attains much lower error rates than those of traditional non-adaptive methods, with less computational cost and less runtime. The findings show better convergence and effective distribution of computing resources without affecting physical fidelity. Altogether, the work introduces a powerful and expandable model of improving the level of the numerical precision in CFD models, and it represents a viable direction towards the high-quality, affordable, modeling of complicated phenomena in fluid flow.