CONTENS Preface to the second edition xv Nomenclature xviii I. Introduction : An Initial Guide to CFD and to this Volume 1 Part 1 : The Mathematical Models for Fluid Flow Simulations at Various Levels of Approximation 21 1. The Basic Equations of Fluid Dynamics 27 2. The Dynamical Levels of Approximation 65 3. The Mathematical Nature of the Flow Equations and Their Boundary Conditions 105 Part 2 : Basic Discretization Techniques 141 4. The Finite Difference Method for Structured Grids 145 5. Finite Volume Method and Conservative Discretization with an Introduction to Finite Element Method203 6. Structured and Unstructured Grid Properties 249 Part 3 : The Analysis of Numerical Schemes 279 7. Consistency, Stability and Error Analysis of Numerical Schemes 283 8. General Properties and High-Resolution Numerical Schemes 337 Part 4 : The Resolution of Numerical Schemes 411 9. Time Integration Methods for Space-discretized Equations 413 10. Iterative Methods for the Resolution of Algebraic Systems 491 Part 5 : App;ications to Inviscid and Viscous Flows 541 11. Numerical Simulation of Inviscid Flows545 12. Numerical Solutions ofViscous Laminar Flows 599 Index 647