Computational Fluid Dynamics

This course covers the fundamental aspects of computational fluid dynamics (CFD), starting with the mathematical classification of partial differential equations and their physical behavior. It provides a deep understanding of elliptic, parabolic, and hyperbolic equations and their applications in aerodynamics and fluid dynamics. For example, it explains how elliptic equations are used for equilibrium problems, while parabolic and hyperbolic equations are used for marching or propagation problems. The course also explores grid generation and discretization in CFD, including problem definition, choice of governing equations, and pre-processing steps. It further delves into the finite difference methods and their application to the discretization of the Laplace equation. The course concludes with an in-depth look at Euler equations and compressible Navier Stokes equations, demonstrating their use in capturing shock waves and expansion waves in compressible flows and handling high-speed flow problems and wave features.