Computational Fluid Dynamics: an Overview of Methods

Fluid flow is a very broad and complicated topic because of the many different aspects and types of applications. I have covered inviscid flow, which occurs when the viscosity is negligible or the velocities are very large, in two previous texts: Differential Equations and Numerical Calculus. I may at some point cover creeping flow, which occurs when the viscosity dominates momentum or the velocities are very small. In this text we will cover the range between these two extremes: when viscosity and momentum are both important, at least in some significant part of the flow field. This is by no means an exhaustive reference on the subject of computational fluid dynamics; rather, it is an introduction and overview, going just far enough to get the reader started along this path with some helpful direction based on years of experience. I have striven to make this a clear presentation, particularly of finite elements, avoiding the traditional esoteric derivations that never seem to arrive at any useful destination. The impetus to undertake this project has arisen from my interacting with many graduate students on Research Gate, who are pursuing CFD and struggling with traditional presentations. You must make decisions when you arrive at a fork in the proverbial road (such as FDM, FVM, or FEM) and I hope this text will provide you with enough information to do that without me imposing my personal preference.