Computational Fluid Dynamics: A Review of Foundations, Methods, and Emerging Machine Learning Approaches

1V.Padma Anuradha, Associate Professor, Department of Mathematics, NTRGDCW(A), Mahabubnagar

Abstract
Computational Fluid Dynamics (CFD) has become an indispensable tool for analyzing and predicting fluid flow behavior across aerospace, automotive, energy, biomedical, and environmental engineering. This review surveys the theoretical foundations of CFD, including the governing Navier-Stokes equations, and examines the principal numerical discretization strategies used to solve them: finite difference, finite volume, and finite element methods. Particular attention is given to turbulence modeling approaches, from Reynolds-Averaged Navier-Stokes (RANS) formulations through Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS), highlighting the trade-offs between computational cost and fidelity. The review then turns to one of the most active areas of contemporary research: the integration of machine learning (ML) and deep learning techniques into CFD workflows. Surrogate modeling, physics-informed neural networks, and data-driven turbulence closures are discussed as mechanisms for accelerating simulations while preserving physical consistency. The paper concludes by outlining persistent challenges, including generalizability, interpretability, and validation of ML-augmented models, and by identifying promising directions for future research, including hybrid physics-ML frameworks and digital twin integration.