Essential Computational Fluid Dynamics
John Wiley & Sons Inc (Verlag)
978-0-470-42329-5 (ISBN)
- Titel erscheint in neuer Auflage
- Artikel merken
This book serves as a complete and self-contained introduction to the principles of Computational Fluid Dynamic (CFD) analysis. It is deliberately short (at approximately 300 pages) and can be used as a text for the first part of the course of applied CFD followed by a software tutorial. The main objectives of this non-traditional format are: 1) To introduce and explain, using simple examples where possible, the principles and methods of CFD analysis and to demystify the `black box’ of a CFD software tool, and 2) To provide a basic understanding of how CFD problems are set and which factors affect the success and failure of the analysis. Included in the text are the mathematical and physical foundations of CFD, formulation of CFD problems, basic principles of numerical approximation (grids, consistency, convergence, stability, and order of approximation, etc), methods of discretization with focus on finite difference and finite volume techniques, methods of solution of transient and steady state problems, commonly used numerical methods for heat transfer and fluid flows, plus a brief introduction into turbulence modeling.
OLEG ZIKANOV is an Associate Professor in the Department of Mechanical Engineering at the University of MichiganDearborn.
PREFACE xv
1 What Is CFD? 1
1.1. Introduction / 1
1.2. Brief History of CFD / 4
1.3. Outline of the Book / 6
References and Suggested Reading / 7
I Fundamentals 9
2 Governing Equations of Fluid Dynamics and Heat Transfer 11
2.1. Preliminary Concepts / 11
2.2. Mass Conservation / 14
2.3. Conservation of Chemical Species / 15
2.4. Conservation of Momentum / 16
2.5. Conservation of Energy / 19
2.6. Equation of State / 21
2.7. Equations in Integral Form / 21
2.8. Equations in Conservation Form / 24
2.9. Equations in Vector Form / 25
2.10. Boundary Conditions / 26
2.10.1. Rigid Wall Boundary Conditions / 27
2.10.2. Inlet and Exit Boundary Conditions / 29
2.10.3. Other Boundary Conditions / 29
References and Suggested Reading / 30
Problems / 30
3 Partial Differential Equations 32
3.1. Model Equations; Formulation of a PDE Problem / 33
3.1.1. Model Equations / 33
3.1.2. Domain, Boundary, and Initial Conditions / 35
3.1.3. Equilibrium and Marching Problems / 36
3.1.4. Examples / 37
3.2. Mathematical Classification of PDE of Second Order / 40
3.2.1. Classification / 40
3.2.2. Hyperbolic Equations / 42
3.2.3. Parabolic Equations / 45
3.2.4. Elliptic Equations / 46
3.3. Numerical Discretization: Different Kinds of CFD / 46
3.3.1. Spectral Methods / 47
3.3.2. Finite Element Methods / 49
3.3.3. Finite Difference and Finite Volume Methods / 49
References and Suggested Reading / 52
Problems / 52
4 Basics of Finite Difference Approximation 55
4.1. Computational Grid / 55
4.1.1. Time Discretization / 55
4.1.2. Space Discretization / 56
4.2. Finite Differences and Interpolation / 57
4.2.1. Approximation of ∂u/∂x / 57
4.2.2. Truncation Error, Consistency, Order of Approximation / 58
4.2.3. Other Formulas for ∂u/∂x: Evaluation of the Order of Approximation / 60
4.2.4. Schemes of Higher Order for First Derivative / 62
4.2.5. Higher-Order Derivatives / 63
4.2.6. Mixed Derivatives / 64
4.2.7. Truncation Error of Linear Interpolation / 66
4.3. Approximation of Partial Differential Equations / 67
4.3.1. Approach and Examples / 67
4.3.2. Interpretation of Truncation Error: Numerical Dissipation and Dispersion / 70
4.3.3. Boundary and Initial Conditions / 73
4.3.4. Consistency of Numerical Approximation / 74
4.3.5. System of Difference Equations / 75
4.3.6. Implicit and Explicit Methods / 76
4.4. Development of Finite Difference Schemes / 78
4.4.1. Taylor Series Expansions / 79
4.4.2. Polynomial Fitting / 82
References and Suggested Reading / 83
Problems / 83
5 Finite Volume Method 86
5.1. Introduction and Integral Formulation / 86
5.1.1. Finite Volume Grid / 87
5.1.2. Global Conservation Property / 89
5.2. Approximation of Integrals / 91
5.2.1. Volume Integrals / 91
5.2.2. Surface Integrals / 92
5.3. Methods of Interpolation / 94
5.3.1. Upwind Interpolation / 95
5.3.2. Linear Interpolation / 96
5.3.3. Upwind Interpolation of Higher Order / 98
5.3.4. Interpolation on Nonorthogonal Grids / 99
5.4. Boundary Conditions / 101
References and Suggested Reading / 102
Problems / 102
6 Stability of Transient Solutions 104
6.1. Introduction and Definition of Stability / 104
6.1.1. Discretization and Round-off Error / 106
6.1.2. Definition / 107
6.2. Stability Analysis / 108
6.2.1. Neumann Method / 108
6.2.2. Matrix Method / 116
6.3. Implicit versus Explicit Schemes—Stability and
Efficiency Considerations / 118
References and Suggested Reading / 120
Problems / 120
7 Application to Model Equations 121
7.1. Linear Convection Equation / 121
7.1.1. Simple Explicit Schemes / 123
7.1.2. Other Schemes / 125
7.2. One-Dimensional Heat Equation / 128
7.2.1. Simple Explicit Scheme / 129
7.2.2. Simple Implicit Scheme / 130
7.2.3. Crank-Nicolson Scheme / 131
7.3. Burgers and Generic Transport Equations / 132
7.4. Method of Lines Approach / 134
7.4.1. Adams Methods / 134
7.4.2. Runge-Kutta Methods / 135
7.5. Implicit Schemes: Solution of Tridiagonal Systems
by Thomas Algorithm / 136
References and Suggested Reading / 140
Problems / 140
II Methods 143
8 Steady-State Problems 145
8.1. Problems Reducible to Matrix Equations / 145
8.1.1. Elliptic PDE / 145
8.1.2. Implicit Integration of Nonsteady Equations / 149
8.2. Direct Methods / 150
8.2.1. Band-Diagonal and Block-Diagonal Matrices / 151
8.2.2. LU Decomposition / 153
8.3. Iterative Methods / 153
8.3.1. General Methodology / 154
8.3.2. Jacobi Iterations / 155
8.3.3. Gauss-Seidel Algorithm / 156
8.3.4. Successive Over- and Underrelaxation / 157
8.3.5. Convergence of Iterative Procedures / 158
8.3.6. Multigrid Methods / 161
8.3.7. Pseudo-transient Approach / 164
8.4. Systems of Nonlinear Equations / 164
8.4.1. Newton’s Algorithm / 165
8.4.2. Iteration Methods Using Linearization / 166
8.4.3. Sequential Solution / 168
References and Suggested Reading / 168
Problems / 169
9 Unsteady Problems of Fluid Flows and Heat Transfer 171
9.1. Introduction / 171
9.2. Compressible Flows / 172
9.2.1. Overview and General Comments / 172
9.2.2. Explicit MacCormack Method / 176
9.2.3. Beam-Warming Method / 178
9.2.4. Upwinding / 182
9.2.5. Methods for Purely Hyperbolic Systems / 185
9.3. Unsteady Conduction Heat Transfer / 187
9.3.1. Simple Methods for Multidimensional Heat Conduction / 188
9.3.2. Approximate Factorization / 189
9.3.3. ADI Method / 191
References and Suggested Reading / 192
Problems / 193
10 Incompressible Flows 196
10.1. General Considerations / 196
10.1.1. Introduction / 196
10.1.2. Role of Pressure / 197
10.2. Discretization Approach / 198
10.2.1. Colocated and Staggered Grids / 200
10.3. Projection Method for Unsteady Flows / 205
10.3.1. Explicit Schemes / 206
10.3.2. Implicit Schemes / 209
10.4. Projection Methods for Steady-State Flows / 212
10.4.1. SIMPLE / 214
10.4.2. SIMPLEC, SIMPLER, and PISO / 216
10.5. Other Methods / 218
10.5.1. Vorticity-Streamfunction Formulation for Two-Dimensional Flows / 218
10.5.2. Artificial Compressibility / 222
References and Suggested Reading / 222
Problems / 223
III Art of CFD 225
11 Turbulence 227
11.1. Introduction / 227
11.1.1. A Few Words About Turbulence / 227
11.1.2. Why Is the Computation of Turbulent Flows Difficult? / 231
11.1.3. Overview of Numerical Approaches / 232
11.2. Direct Numerical Simulation (DNS) / 234
11.2.1. Homogeneous Turbulence / 234
11.2.2. Inhomogeneous Turbulence / 237
11.3. Reynolds-Averaged Navier-Stokes (RANS) Models / 238
11.3.1. Reynolds-Averaged Equations / 240
11.3.2. Eddy Viscosity Hypothesis / 241
11.3.3. Algebraic Models / 242
11.3.4. Two-Equation Models / 243
11.3.5. Numerical Implementation of RANS Models / 246
11.4. Large-Eddy Simulation (LES) / 249
11.4.1. Filtered Equations / 250
11.4.2. Closure Models / 253
11.4.3. Implementation of LES in CFD Analysis: Numerical Resolution and Near-Wall Treatment / 255
References and Suggested Reading / 258
Problems / 259
12 Computational Grids 261
12.1. Introduction: Need for Irregular and Unstructured Grids / 261
12.2. Irregular Structured Grids / 264
12.2.1. Generation by Coordinate Transformation / 264
12.2.2. Examples / 266
12.2.3. Grid Quality / 268
12.3. Unstructured Grids / 269
12.3.1. Grid Generation / 271
12.3.2. Finite Volume Discretization on Unstructured Grids / 272
12.3.3. Cell Topology / 274
12.3.4. Grid Quality / 275
References and Suggested Reading / 278
Problems / 278
13 Conducting CFD Analysis 280
13.1. Overview: Setting and Solving a CFD Problem / 280
13.2. Errors and Uncertainty / 283
13.2.1. Errors in CFD Analysis / 283
13.2.2. Verification and Validation / 290
13.3. Adaptive Grids / 293
References and Suggested Reading / 295
INDEX 297
| Zusatzinfo | Photos: 3 B&W, 0 Color; Drawings: 127 B&W, 0 Color |
|---|---|
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 160 x 241 mm |
| Gewicht | 558 g |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik |
| Technik ► Maschinenbau | |
| ISBN-10 | 0-470-42329-3 / 0470423293 |
| ISBN-13 | 978-0-470-42329-5 / 9780470423295 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
aus dem Bereich
