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 Plows
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
5.2 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-Stokes Equations
7.1.1 Discretization of Convective and Viscous Terms
7.1.2 Discretization of Pressure Terms and Body Forces
7.1.3 Conservation Properties
7.2 Choice of Variable Arrangement on the Grid
7.2.1 Colocated Arrangement
7.2.2 Staggered Arrangements
7.3 Calculation of the Pressure
7.3.1 The Pressure Equation and its Solution
7.3.2 A Simple Explicit Time Advance Scheme
7.3.3 A Simple Implicit Time Advance Method
7.3.4 Implicit Pressure-Correction Methods
7.4 Other Methods
7.4.1 Fractional Step Methods
7.4.2 Streamfunction-Vorticity Methods
7.4.3 Artificial Compressibility Methods
7.5 Solution Methods for the Navier-Stokes Equations
7.5.1 Implicit Scheme Using Pressure-Correction and a Stag-gered Grid
7.5.2 Treatment of Pressure for Colocated Variables
7.5.3 SIMPLE Algorithm for a Colocated Variable Arrange-ment
7.6 Note on Pressure and Incompressibility
7.7 Boundary Conditions for the Navier-Stokes Equations
7.8 Examples
8.Complex Geometries
8.1 The Choice of Grid
8.1.1 Stepwise Approximation Using Regular Grids
8.1.2 Overlapping Grids
8.1.3 Boundary-Fitted Non-Orthogonal Grids
8.2 Grid Generation
8.3 The Choice of Velocity Components
8.3.1 Grid-Oriented Velocity Components
8.3.2 Cartesian Velocity Components
8.4 The Choice of Variable Arrangement
8.4.1 Staggered Arrangements
8.4.2 Colocated Arrangement
8.5 Finite Difference Methods
8.5.1 Methods Based on Coordinate Transformation
8.5.2 Method Based on Shape Functions
8.6 Finite Volume Methods
8.6.1 Approximation of Convective Fluxes
8.6.2 Approximation of Diffusive Fluxes
8.6.3 Approximation of Source Terms
8.6.4 Three-Dimensional Grids
8.6.5 Block-Structured Grids
8.6.6 Unstructured Grids
8.7 Control-Volume-Based Finite Element Methods
8.8 Pressure-Correction Equation
8.9 Axi-Symmetric Problems
8.10 Implementation of Boundary Conditions
8.10.1 Inlet
8.10.2 Outlet
8.10.3 Impermeable Walls
8.10.4 Symmetry Planes
8.10.5 Specified Pressure
8.11 Examples
9.Turbulent Flows
9.1 Introduction
9.2 Direct Numerical Simulation(DNS）
9.2.1 Example: Spatial Decay of Grid Turbulence
9.3 Large Eddy Simulation(LES）
9.3.1 Smagorinsky and Related Models
9.3.2 Dynamic Models
9.3.3 Deconvolution Models
9.3.4 Example: Flow Over a Wall-Mounted Cube
9.3.5 Example: Stratified Homogeneous Shear Flow
9.4 RANS Models
9.4.1 Reynolds-Averaged Navier-Stokes(RANS)Equations
9.4.2 Simple Turbulence Models and their Application
9.4.3 The v2f Model
9.4.4 Example: Flow Around an Engine Valve
9.5 Reynolds Stress Models
9.6 Very Large Eddy Simulation
10.Compressible Flow
10.1 Introduction
10.2 Pressure-Correction Methods for Arbitrary Mach Number
10.2.1 Pressure-Velocity-Density Coupling
10.2.2 Boundary Conditions
10.2.3 Examples
10.3 Methods Designed for Compressible Flow
10.3.1 An Overview of Some Specific Methods
11.Efficiency and Accuracy Improvement
11.1 Error Analysis and Estimation
11.1.1 Description of Errors
11.1.2 Estimation of Errors
11.1.3 Recommended Practice for CFD Uncertainty Analysis
11.2 Grid quality and optimization
11.3 Multigrid Methods for Flow Calculation
11.4 Adaptive Grid Methods and Local Grid Refinement
11.5 Parallel Computing in CFD
11.5.1 Iterative Schemes for Linear Equations
11.5.2 Domain Decomposition in Space
11.5.3 Domain Decomposition in Time
11.5.4 Efficiency of Parallel Computing
12.Special Topics
12.1 Introduction
12.2 Heat and Mass Transfer
12.3 Flows With Variable Fluid Properties
12.4 Moving Grids
12.5 Free-Surface Flows
12.5.1 Interface-Tracking Methods
12.5.2 Hybrid Methods
12.6 Meteorological and Oceanographic Applications
12.7 Multiphase flows
12.8 Combustion
A.Appendices
A.1 List of Computer Codes and How to Access Them
A.2 List of Frequently Used Abbreviations
References
Index
