Computational Fluid Dynamics: Numerical Methods, Turbulence Modeling, and Emerging Applications

Abstract

Computational Fluid Dynamics (CFD) has evolved over the past six decades from a specialized research tool into an indispensable pillar of engineering design and scientific discovery. By numerically solving the governing equations of fluid motion, CFD allows engineers and scientists to predict flow behavior in situations where analytical solutions are intractable and physical experimentation is costly, dangerous, or simply impossible. This paper presents a comprehensive review of the discipline, beginning with the mathematical foundations rooted in the Navier-Stokes equations and progressing through the principal discretization strategies — finite difference,
finite volume, finite element, and spectral methods.