Computational Fluid Dynamics: Principles and Applications (eBook)

Front Cover 1
Computational Fluid Dynamics: Principles and Applications 4
Copyright Page 5
Contents 6
Acknowledgements 12
List of Symbols 14
Abbreviations 20
Chapter 1. Introduction 22
Chapter 2. Governing Equations 26
2.1 The Flow and its Mathematical Description 26
2.2 Conservation Laws 29
2.3 Viscous Stresses 34
2.4 Complete System of the Navier-Stokes Equations 37
Bibliography 47
Chapter 3. Principles of Solution of the Governing Equations 50
3.1 Spatial Discretisation 53
3.2 Temporal Discretisation 66
3.3 Turbulence Modelling 74
3.4 Initial and Boundary Conditions 77
Bibliography 79
Chapter 4. Spatial Discretisation. Structured Finite Volume Schemes 96
4.1 Geometrical Quantities of a Control Volume 100
4.2 General Discretisation Methodologies 104
4.3 Discretisation of Convective Fluxes 114
4.4 Discretisation of Viscous Fluxes 137
Bibliography 141
Chapter 5. Spatial Discretisation: Unstructured Finite Volume Schemes 150
5.1 Geometrical Quantities of a Control Volume 155
5.2 General Discretisation Methodologies 159
5.3 Discretisation of Convective Fluxes 171
5.4 Discretisation of Viscous Fluxes 190
Bibliography 195
Chapter 6. Temporal Discretisation 202
6.1 Exphcit Time-Stepping Schemes 203
6.2 Implicit Time-Stepping Schemes 211
6.3 Methodologies for Unsteady Flows 233
Bibliography 237
Chapter 7. Turbulence Modelling 246
7.1 Basic Equations of Turbulence 249
7.2 First-Order Closures 259
7.3 Large-Eddy Simulation 269
Bibliography 277
Chapter 8. Boundary Conditions 288
8.1 Concept of Dummy Cells 289
8.2 Solid Wall 291
8.3 Farfield 298
8.4 Inlet/Outlet Boundary 304
8.5 Symmetry Plane 306
8.6 Coordinate Cut 307
8.7 Periodic Boundaries 308
8.8 Interface Between Grid Blocks 311
8.9 Flow Gradients at Boundaries of Unstructured Grids 314
Bibliography 315
Chapter 9. Acceleration Techniques 320
9.1 Local Time-Stepping 320
9.2 Enthalpy Damping 321
9.3 Residual Smoothing 322
9.4 Multigrid 326
9.5 Preconditioning for Low Mach Numbers 341
Bibliography 345
Chapter 10. Consistency, Accuracy and Stability 352
10.1 Consistency Requirements 353
10.2 Accuracy of Discretisation 354
10.3 Von Neumann Stability Analysis 355
Bibliography 371
Chapter 11. Principles of Grid Generation 374
11.1 Structured Grids 377
11.2 Unstructured Grids 388
Bibliography 405
Chapter 12. Description of the Source Codes 414
12.1 Programs for Stability Analysis 416
12.2 Structured 1-D Grid Generator 416
12.3 Structured 2-D Grid Generators 417
12.4 Structured to Unstructured Grid Converter 417
12.5 Quasi 1-D Euler Solver 417
12.6 Structured 2-D Euler Solver 419
12.7 Unstructured 2-D Euler Solver 421
Bibliography 421
A. Appendix 422
A.1 Governing Equations in Differential Form 422
A.2 Mathematical Character of the Governing Equations 428
A.3 Navier-Stokes Equations in Rotating Frame of Reference 432
A.4 Navier-Stokes Equations Formulated for Moving Grids 435
A.5 Thin Shear Layer Approximation 437
A.6 Parabolised Navier-Stokes Equations 439
A.7 Convective Flux Jacobian 440
A.8 Viscous Flux Jacobian 442
A.9 Transformation from Conservative to Characteristic Variables 445
A.10 GMRES Algorithm 448
A.11 Tensor Notation 452
Bibliography 453
Index 456