本书讲述了用计算机解决流体力学问题的技巧，包括计算流体力学中的高级技巧，比如湍流的大漩涡模拟、多格方法、平行计算、移动格、结构、块结构和非结构边界适用格，自由曲面流。

Preface
1.Basic Concepts of Fluid Flow
1.1 Introduction
1.2 Conservation Principles
1.3 Mass Conservation
1.4 Momentum Conservation
1.5 Conservation of Scalar Quantities
1.6 Dimensionless Form of Equations
1.7 Simplified Mathematical Models
1.7.1 Incompressible Flow
1.7.2 Inviscid (Euler)Flow
1.7.3 Potential Flow
1.7.4 Creeping(Stokes)Flow
1.7.5 Boussinesq Approximation
1.7.6 Boundary Layer Approximation
1.7.7 Modeling of Complex Flow Phenomena
1.8 Mathematical Classification of Flows
1.8.1 Hyperbolic Flows
1.8.2 Parabolic Flows
1.8.3 Elliptic Flows
1.8.4 Mixed Flow Types
1.9 Plan of This Book
2.Introduction to Numerical Methods
2.1 Approaches to Fluid Dynamical Problems
2.2 What is CFD
2.3 Possibilities and Limitations of Numerical Methods
2.4 Components of a Numerical Solution Method
2.4.1 Mathematical Model
2.4.2 .Discretization Method
2.4.3 Coordinate and Basis Vector Systems
2.4.4 Numerical Grid
2.4.5 Finite Approximations
2.4.6 Solution Method
2.4.7 Convergence Criteria
2.5 Properties of Numerical Solution Methods
2.5.1 Consistency
2.5.2 Stability
2.5.3 Convergence
2.5.4 Conservation
2.5.5 Boundedness
2.5.6 Realizability
2.5.7 Accuracy
2.6 Discretization Approaches
2.6.1 Finite Difference Method
2.6.2 Finite Volume Method
2.6.3 Finite Element Method
3.Finite Difference Methods
3.1 Introduction
3.2 Basic Concept
3.3 Approximation of the First Derivative
3.3.1 Taylor Series Expansion
3.3.2 Polynomial Fitting
3.3.3 Compact Schemes
3.3.4 Non-Uniform Grids
3.4 Approximation of the Second Derivative
3.5 Approximation of Mixed Derivatives
3.6 Approximation of Other Terms
3.7 Implementation of Boundary Conditions
3.8 The Algebraic Equation System
3.9 Discretization Errors
3.10 An Introduction to Spectral Methods
3.10.1 Basic Concept
3.10.2 Another View of Discretization Error
3.11 Example
4.Finite Volume Methods
4.1 Introduction
4.2 Approximation of Surface Integrals
4.3 Approximation of Volume Integrals
4.4 Interpolation and Differentiation Practices
4.4.1 Upwind Interpolation (UDS)
4.4.2 .Linear Interpolation(CDS)
4.4.3 Quadratic Upwind Interpolation(QUICK)
4.4.4 Higher-Order Schemes
4.4.5 Other Schemes
4.5 Implementation of Boundary Conditions
4.6 The Algebraic Equation System
4.7 Examples
5.Solution of Linear Equation Systems
5.1 Introduction
Direct Methods
5.2.1 Gauss Elimination
5.2.2 LU Decomposition
5.2.3 Tridiagonal Systems
5.2.4 Cyclic Reduction
5.3 Iterative Methods
5.3.1 Basic Concept
5.3.2 Convergence
5.3.3 Some Basic Methods
5.3.4 Incomplete LU Decomposition:Stone's Method
5.3.5 ADI and Other Splitting Methods
5.3.6 Conjugate Gradient Methods
5.3.7 Biconjugate Gradients and CGSTAB
5.3.8 Multigrid Methods
5.3.9 Other Iterative Solvers
5.4 Coupled Equations and Their Solution
5.4.1 Simultaneous Solution
5.4.2 Sequential Solution
5.4.3 Under-Relaxation
5.5 Non-Linear Equations and their Solution
5.5.1 Newton-like Techniques
5.5.2 Other Techniques
5.6 Deferred-Correction Approaches
5.7 Convergence Criteria and Iteration Errors
5.8 Examples
6.Methods for Unsteady Problems
6.1 Introduction
6.2 Methods for Initial Value Problems in ODEs
6.2.1 Two-Level Methods
6.2.2 Predictor-Corrector and Multipoint Methods
6.2.3 Runge-Kutta Methods
6.2.4 Other Methods
6.3 Application to the Generic Transport Equation
6.3.1 Explicit Methods
6.3.2 Implicit Methods
6.3.3 Other Methods
6.4 .Examples
7.Solution of the Navier-Stokes Equations
7.1 Special Features of the Navier-Sto