Fundamental Physical and Model Equations -- The Fluid Flow Equations -- The Viscous Fluid Flow Equations -- Curvilinear Coordinates and Transformed Equations -- Overview of Various Formulations and Model Equations -- Basic Principles in Numerical Analysis -- Time Integration Methods -- Numerical Linear Algebra -- Solution Approaches -- Compressible and Preconditioned-Compressible Solvers -- The Artificial Compressibility Method -- Projection Methods: The Basic Theory and the Exact Projection Method -- Approximate Projection Methods -- Modern High-Resolution Methods -- to Modern High-Resolution Methods -- High-Resolution Godunov-Type Methods for Projection Methods -- Centered High-Resolution Methods -- Riemann Solvers and TVD Methods in Strict Conservation Form -- Beyond Second-Order Methods -- Applications -- Variable Density Flows and Volume Tracking Methods -- High-Resolution Methods and Turbulent Flow Computation.Dimitris Drikakis is Professor and Head of Fluid Mechanics and Computational Science Group at Cranfield University, United Kingdom. His research interests include computational methods, modeling of turbulent flows, unsteady aerodynamics, flow instabilities, shock waves and gas dynamics, biological flows, computational nanotechnology and nanoscience, and high performance computing. William Rider is project and team leader in the Continuum Dynamics Group in the Computer and Computational Sciences Division of the Los Alamos National Laboratory (LANL), U.S.A. His principal interest is computational physics with an emphasis on fluid dynamics, radiation transport, turbulent mixing, shock physics, code verification, code validation and models for turbulence. This book covers the basic techniques for simulating incompressible and low-speed flows with high fidelity in conjunction with high-resolution methods. This includes techniques for steady and unsteady flows with high-order time integration and multigrid methods, as well as specific issues associated with interfacial and turbulent flows. The book is addressed to a broad readership, including engineers and scientists concerned with the development or application of computational methods for fluid flow problems in: Mechanical, Aerospace, Civil and Chemical Engineering, Biological Flows, Atmospheric and Oceanographic Applications as well as other Environmental disciplines. It can be used for teaching postgraduate courses on Computational Fluid Dynamics and Numerical Methods in Engineering and Applied Mathematics, and can also be used as a complementary textbook in undergraduate CFD courses.