Introduction to Computational Fluid Dynamics is a textbook for advanced undergraduate and first year graduate students in mechanical, aerospace and chemical engineering. The book emphasizes understanding CFD through physical principles and examples. The author follows a consistent philosophy of control volume formulation of the fundamental laws of fluid motion and energy transfer, and introduces a novel notion of 'smoothing pressure correction' for solution of flow equations on collocated grids within the framework of the well-known SIMPLE algorithm. The subject matter is developed by considering pure conduction/diffusion, convective transport in 2-dimensional boundary layers and in fully elliptic flow situations and phase-change problems in succession. The book includes chapters on discretization of equations for transport of mass, momentum and energy on Cartesian, structured curvilinear and unstructured meshes, solution of discretised equations, numerical grid generation and convergence enhancement. Practising engineers will find this particularly useful for reference and for continuing education.
Author(s): Anil W. Date
Publisher: Cambridge University Press
Year: 2005
Language: English
Pages: 398
Tags: Механика;Механика жидкостей и газов;Гидрогазодинамика;
Cover......Page 1
About......Page 2
Introduction to Computational Fluid Dynamics......Page 4
9780521853262......Page 5
Contents......Page 8
Nomenclature......Page 14
Preface......Page 18
1.1 CFD Activity ......Page 22
1.2 Transport Equations ......Page 23
1.3 Numerical Versus Analytical Solutions ......Page 26
1.4 Main Task ......Page 27
1.5 A Note on Navier–Stokes Equations ......Page 30
1.6 Outline of the Book ......Page 33
Exercises ......Page 34
2.2 1D Conduction Equation ......Page 38
2.3 Grid Layout ......Page 40
2.4 Discretisation ......Page 41
2.4.1 TSE Method ......Page 42
2.4.2 IOCV Method ......Page 44
2.5 Stability and Convergence ......Page 45
2.5.1 Explicit Procedure ψ = 0......Page 46
2.5.2 Partially Implicit Procedure 0 < ψ < 1......Page 49
2.5.3 Implicit Procedure ψ = 1......Page 50
2.6 Making Choices ......Page 52
2.7 Dealing with Nonlinearities ......Page 53
2.7.2 Nonlinear Coefficients ......Page 54
2.7.3 Boundary Conditions ......Page 56
2.7.4 Underrelaxation ......Page 58
2.8.2 Tridiagonal Matrix Algorithm ......Page 59
2.8.3 Applications ......Page 61
2.9 Problems from Related Fields ......Page 66
Exercises ......Page 68
3.2 Exact Solution ......Page 76
3.3 Discretisation ......Page 78
3.4 Upwind Difference Scheme ......Page 80
3.5 Comparison of CDS, UDS, and Exact Solution ......Page 81
3.6 Numerical False Diffusion ......Page 82
3.8 Total Variation Diminishing Scheme ......Page 84
3.9.1 Exact Solution ......Page 86
3.9.2 Explicit Finite-Difference Form ......Page 87
3.9.3 Implicit Finite-Difference Form ......Page 88
Exercises ......Page 89
4.1 Governing Equations ......Page 92
4.2 Adaptive Grid ......Page 94
4.3 Transformation to (x, ω) Coordinates......Page 95
4.4 Discretisation ......Page 97
4.5 Determination of ω, y, and r......Page 100
4.6.1 Symmetry ......Page 101
4.6.2 Wall ......Page 102
4.6.3 Free Stream ......Page 103
4.7.1 Pressure Gradient ......Page 106
4.7.2 Q''' and R_k......Page 107
4.8 Treatment of Turbulent Flows ......Page 108
4.8.1 Mixing Length Model ......Page 109
4.8.2 e-ε Model......Page 110
4.9.1 Calculation Sequence ......Page 112
4.9.2 Initial Conditions ......Page 113
4.10 Applications ......Page 114
Exercises ......Page 122
5.1.1 Main Task ......Page 126
5.1.2 Solution Strategy ......Page 127
5.2.1 Main Idea ......Page 130
5.2.2 Discretisation ......Page 131
5.2.3 Pressure-Correction Equation ......Page 133
5.2.4 Further Simplification ......Page 138
5.2.5 Overall Calculation Procedure ......Page 140
5.3.1 Iterative Solvers ......Page 141
5.3.2 Evaluation of Residuals ......Page 142
5.3.3 Underrelaxation ......Page 143
5.3.4 Boundary Conditions for Φ......Page 144
5.3.5 Boundary Condition for p'_m......Page 146
5.3.6 Node Tagging ......Page 147
5.4.1 LRE Model ......Page 149
5.4.2 HRE Model ......Page 150
5.5 Notion of Smoothing Pressure Correction ......Page 154
5.6 Applications ......Page 160
Exercises ......Page 173
6.1.1 Curvilinear Grids ......Page 182
6.1.2 Unstructured Grids ......Page 183
6.2.1 Coordinate Transformation ......Page 185
6.2.2 Transport Equation ......Page 186
6.2.3 Interpretation of Terms ......Page 187
6.2.4 Discretisation ......Page 189
6.2.5 Pressure-Correction Equation ......Page 191
6.2.6 Overall Calculation Procedure ......Page 192
6.2.7 Node Tagging and Boundary Conditions ......Page 193
6.3.1 Main Task ......Page 195
6.3.2 Gauss’s Divergence Theorem ......Page 198
6.3.3 Construction of a Line Structure ......Page 200
6.3.4 Convective Transport ......Page 201
6.3.5 Diffusion Transport ......Page 202
6.3.6 Interim Discretised Equation ......Page 203
6.3.7 Interpolation of Φ at P_2, E_2, a, and b......Page 204
6.3.8 Final Discretised Equation ......Page 205
6.3.10 Boundary Conditions ......Page 207
6.3.11 Pressure-Correction Equation ......Page 211
6.3.12 Method of Solution ......Page 213
6.3.13 Overall Calculation Procedure ......Page 214
6.4 Applications ......Page 215
6.5 Closure ......Page 228
Exercises ......Page 230
7.1 Introduction ......Page 235
7.2.1 Exact Solution ......Page 237
7.2.2 Simple Numerical Solution ......Page 238
7.2.3 Numerical Solution Using TDMA ......Page 242
7.2.4 Accurate Solutions on a Coarse Grid ......Page 243
7.3 1D Problems for Impure Substances ......Page 246
Exercises ......Page 251
8.2.1 1D Domains ......Page 254
8.2.2 2D Domains ......Page 255
8.3.1 1D Domains ......Page 256
8.3.2 2D Domains ......Page 258
8.3.3 Inversion of Determinant Equations ......Page 259
8.4.1 Main Specifications ......Page 262
8.4.2 Stretching Functions ......Page 264
8.4.4 Solution Procedure ......Page 265
8.4.5 Applications ......Page 266
8.5.1 Main Task ......Page 269
8.5.2 Domains with (i , j) Structure......Page 270
8.5.3 Automatic Grid Generation ......Page 271
Exercises ......Page 274
9.1 Convergence Rate ......Page 280
9.2 Block Correction ......Page 282
9.3 Method of Two Lines ......Page 283
9.4 Stone’s Method ......Page 286
9.5 Applications ......Page 290
Exercises ......Page 293
Appendix A. Derivation of Transport Equations ......Page 294
Appendix B. 1D Conduction Code ......Page 305
Appendix C. 2D Cartesian Code ......Page 327
Bibliography ......Page 390
Index ......Page 396
