Part I Basic Thoughts and Equations 1 Philosophy of Computational Fluid Dynamics 1.1 Computational Fluid Dynamics:Why? 1.2 Computational Fluid Dynamics as a Research Tool 1.3 Computational Fluid Dynamics as a Design Tool 1.4 The Impact of Computational Fluid Dynamics-Some Other 1.5 Computational Fluid Dynamics:What Is It? 1.6 The Purpose of This Book 2 The Governing Equations of Fluid Dynamics: Their Derivation,a Discussion of Their Physical Meaning,and a Presentation of Forms Particularly Suitable to CFD 2.1 Introduction 2.2 Models of the Flow 2.3 The Substantial Derivative(Time Rate of Change Following a Moving Fluid Element 2.4 The Divergence of the Velocity:Its Physical Meaning 2.5 The Continuity Equation 2.6 The Monetum Equation 2.7 The Energy Equation 2.8 Summary of the Governing Equations for Fluid Dynamics 2.9 Physical Boundary Conditions …… 3 Mathematical Behavior of Partial Differential Equations: The Impact on CFD Part II Basics of the Numerics 4 Basic Aspects of Discretization 5 Grids with Appropriate Transformations 6 Some Simple CFD Techniques: A Beginning Part III Some Applications 7 Numerical Solutions of Quasi-One-Dimensional Nozzle Flows 8 Numerical Solution of a Two-Dimensional Supersonic Flow: Prandtl-Meyer Expansion Wave 9 Incompressible Couette Flow: Numerical Solutions by Means of an Implicit Method and the Pressure Correction Method 10 Supersonic Flow over a Flat Plate: Numerical Solution by Solving the Complete Navier-Stodes Equations Part IV Other Topics 11 Some Advanced Topics in Modern CFD: A Discussion 12 The Future of CFD