This book aims to provide a foundation to CFD which finds application in solving leading edge research problems. It includes both classical and recent methods of solving high Reynolds number incompressible flows. The first four chapters deal with the governing equations and discussions on ranges of temporal and spatial scales. This is followed by classical methods for PDEs, coordinate transformations and grid generation. A full chapter is devoted to spectral analysis tools developed by the author, and aliasing error which is least understood but important for DNS/LES. The last three chapters provide higher order methods, discussions on higher accuracy finite volume methods and their comparison to finite element methods. In the last chapter, applications of some of the methods highlighting the issues of unsteady and transitional/turbulent flows are presented.
Preface / Basic Ideas of Computational Fluid Mechanics / Governing Equations of Fluid Mechanics / Classification of Quasi-Linear PDEs / Additional Issues of CFD: Space-Time Resolution of Flows / Discretization of Partial Differential Equations / Solution Methods for Parabolic PDEs and their Analysis / Solution Method for Elliptic PDEs / Solution of Hyperbolic PDEs / Curvillinear Coordinates and Grid Generation / Spectral Analysis of Numerical Schemes and Aliasing Error / High Order Methods / Introduction to Finite Volume and Finite Element Methods / Solution of Navier-Stokes Equation / Appendices / Index