Introduction to Computational Fluid Dynamics

"This book introduces all the primary components for learning and practicing computational fluid dynamics (CFD). The book is written for final year undergraduates and/or graduate students in mechanical, chemical, and aeronautical engineering who have undergone basic courses in thermodynamics, fluid mechanics, and heat and mass transfer."--BOOK JACKET.

Nomenclature

xiii

Preface

xvii

Introduction

1

(16)

CFD Activity

1

(1)

Transport Equations

2

(3)

Numerical Versus Analytical Solutions

5

(1)

Main Task

6

(3)

A Note on Navier-Stokes Equations

9

(3)

Outline of the Book

12

(5)

Exercises

13

(4)

1D Heat Conduction

17

(38)

Introduction

17

(1)

1D Conduction Equation

17

(2)

Grid Layout

19

(1)

Discretisation

20

(4)

TSE Method

21

(2)

IOCV Method

23

(1)

Stability and Convergence

24

(7)

Explicit Procedure ψ = 0

25

(3)

Partially Implicit Procedure 0 < ψ < 1

28

(1)

Implicit Procedure ψ = 1

29

(2)

Making Choices

31

(1)

Dealing with Nonlinearities

32

(6)

Nonlinear Sources

33

(1)

Nonlinear Coefficients

33

(2)

Boundary Conditions

35

(2)

Underrelaxation

37

(1)

Methods of Solution

38

(7)

Gauss-Seidel Method

38

(1)

Tridiagonal Matrix Algorithm

38

(2)

Applications

40

(5)

Problems from Related Fields

45

(10)

Exercises

47

(8)

1D Conduction--Convection

55

(16)

Introduction

55

(1)

Exact Solution

55

(2)

Discretisation

57

(2)

Upwind Difference Scheme

59

(1)

Comparison of CDS, UDS, and Exact Solution

60

(1)

Numerical False Diffusion

61

(2)

Hybrid and Power-Law Schemes

63

(1)

Total Variation Diminishing Scheme

63

(2)

Stability of the Unsteady Equation

65

(6)

Exact Solution

65

(1)

Explicit Finite-Difference Form

66

(1)

Implicit Finite-Difference Form

67

(1)

Exercises

68

(3)

Boundary Layers

71

(34)

Governing Equations

71

(2)

Adaptive Grid

73

(1)

Transformation to (x, ω) Coordinates

74

(2)

Discretisation

76

(3)

Determination of ω, y, and r

79

(1)

Boundary Conditions

80

(5)

Symmetry

80

(1)

Wall

81

(1)

Free Stream

82

(3)

Source Terms

85

(2)

Pressure Gradient

85

(1)

Q''' and Rk

86

(1)

Treatment of Turbulent Flows

87

(4)

Mixing Length Model

88

(1)

e--ε Model

89

(2)

Free-Shear Flows

91

(1)

Overall Procedure

91

(2)

Calculation Sequence

91

(1)

Initial Conditions

92

(1)

Choice of Step Size and Iterations

93

(1)

Applications

93

(12)

Exercises

101

(4)

2D Convection -- Cartesian Grids

105

(56)

Introduction

105

(4)

Main Task

105

(1)

Solution Strategy

106

(3)

Simple -- Collocated Grids

109

(11)

Main Idea

109

(1)

Discretisation

110

(2)

Pressure-Correction Equation

112

(5)

Further Simplification

117

(2)

Overall Calculation Procedure

119

(1)

Method of Solution

120

(8)

Iterative Solvers

120

(1)

Evaluation of Residuals

121

(1)

Underrelaxation

122

(1)

Boundary Conditions for Φ

123

(2)

Boundary Condition for P'm

125

(1)

Node Tagging

126

(2)

Treatment of Turbulent Flows

128

(5)

LRE Model

128

(1)

HRE Model

129

(4)

Notion of Smoothing Pressure Correction

133

(6)

Applications

139

(22)

Exercises

152

(9)

2D Convection -- Complex Domains

161

(53)

Introduction

161

(3)

Curvilinear Grids

161

(1)

Unstructured Grids

162

(2)

Curvilinear Grids

164

(10)

Coordinate Transformation

164

(1)

Transport Equation

165

(1)

Interpretation of Terms

166

(2)

Discretisation

168

(2)

Pressure-Correction Equation

170

(1)

Overall Calculation Procedure

171

(1)

Node Tagging and Boundary Conditions

172

(2)

Unstructured Meshes

174

(20)

Main Task

174

(3)

Gauss's Divergence Theorem

177

(2)

Construction of a Line Structure

179

(1)

Convective Transport

180

(1)

Diffusion Transport

181

(1)

Interim Discretised Equation

182

(1)

Interpolation of Φ at P2, E2, a, and b

183

(1)

Final Discretised Equation

184

(2)

Evaluation of Nodal Gradients

186

(1)

Boundary Conditions

186

(4)

Pressure-Correction Equation

190

(2)

Method of Solution

192

(1)

Overall Calculation Procedure

193

(1)

Applications

194

(13)

Closure

207

(7)

Exercises

209

(5)

Phase Change

214

(19)

Introduction

214

(2)

1D Problems for Pure Substances

216

(9)

Exact Solution

216

(1)

Simple Numerical Solution

217

(4)

Numerical Solution Using TDMA

221

(1)

Accurate Solutions on a Coarse Grid

222

(3)

1D Problems for Impure Substances

225

(8)

Exercises

230

(3)

Numerical Grid Generation

233

(26)

Introduction

233

(1)

Algebraic Grid Generation

233

(2)

1D Domains

233

(1)

2D Domains

234

(1)

Differential Grid Generation

235

(6)

1D Domains

235

(2)

2D Domains

237

(1)

Inversion of Determinant Equations

238

(3)

Sorenson's Method

241

(7)

Main Specifications

241

(2)

Stretching Functions

243

(1)

Discretisation

244

(1)

Solution Procedure

244

(1)

Applications

245

(3)

Unstructured Mesh Generation

248

(11)

Main Task

248

(1)

Domains with (i, j) Structure

249

(1)

Automatic Grid Generation

250

(3)

Exercises

253

(6)

Convergence Enhancement

259

(14)

Convergence Rate

259

(2)

Block Correction

261

(1)

Method of Two Lines

262

(3)

Stone's Method

265

(4)

Applications

269

(4)

Exercises

272

(1)

Appendix A. Derivation of Transport Equations

273

(11)

Appendix B. 1D Conduction Code

284

(22)

Appendix C. 2D Cartesian Code

306

(63)

Bibliography

369

(6)

Index

375

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Introduction to Computational Fluid Dynamics

Summary

Table of Contents

Supplemental Materials