Computational Fluid Dynamics: Principles and Applications: Principles and Applications
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Table of contents
- Contentsv
- Acknowledgementsxi
- List of Symbolsxiii
- Abbreviationsxix
- Chapter 1. Introduction1
- Chapter 2. Governing Equations5
- 2.1 The Flow and its Mathematical Description5
- 2.2 Conservation Laws8
- 2.3 Viscous Stresses13
- 2.4 Complete System of the Navier-Stokes Equations16
- Bibliography26
- Chapter 3. Principles of Solution of the Governing Equations29
- 3.1 Spatial Discretisation32
- 3.2 Temporal Discretisation45
- 3.3 Turbulence Modelling53
- 3.4 Initial and Boundary Conditions56
- Bibliography58
- Chapter 4. Spatial Discretisation. Structured Finite Volume Schemes75
- 4.1 Geometrical Quantities of a Control Volume79
- 4.2 General Discretisation Methodologies83
- 4.3 Discretisation of Convective Fluxes93
- 4.4 Discretisation of Viscous Fluxes116
- Bibliography120
- Chapter 5. Spatial Discretisation: Unstructured Finite Volume Schemes129
- 5.1 Geometrical Quantities of a Control Volume134
- 5.2 General Discretisation Methodologies138
- 5.3 Discretisation of Convective Fluxes150
- 5.4 Discretisation of Viscous Fluxes169
- Bibliography174
- Chapter 6. Temporal Discretisation181
- 6.1 Exphcit Time-Stepping Schemes182
- 6.2 Implicit Time-Stepping Schemes190
- 6.3 Methodologies for Unsteady Flows212
- Bibliography216
- Chapter 7. Turbulence Modelling225
- 7.1 Basic Equations of Turbulence228
- 7.2 First-Order Closures238
- 7.3 Large-Eddy Simulation248
- Bibliography256
- Chapter 8. Boundary Conditions267
- 8.1 Concept of Dummy Cells268
- 8.2 Solid Wall270
- 8.3 Farfield277
- 8.4 Inlet/Outlet Boundary283
- 8.5 Symmetry Plane285
- 8.6 Coordinate Cut286
- 8.7 Periodic Boundaries287
- 8.8 Interface Between Grid Blocks290
- 8.9 Flow Gradients at Boundaries of Unstructured Grids293
- Bibliography294
- Chapter 9. Acceleration Techniques299
- 9.1 Local Time-Stepping299
- 9.2 Enthalpy Damping300
- 9.3 Residual Smoothing301
- 9.4 Multigrid305
- 9.5 Preconditioning for Low Mach Numbers320
- Bibliography324
- Chapter 10. Consistency, Accuracy and Stability331
- 10.1 Consistency Requirements332
- 10.2 Accuracy of Discretisation333
- 10.3 Von Neumann Stability Analysis334
- Bibliography350
- Chapter 11. Principles of Grid Generation353
- 11.1 Structured Grids356
- 11.2 Unstructured Grids367
- Bibliography384
- Chapter 12. Description of the Source Codes393
- 12.1 Programs for Stability Analysis395
- 12.2 Structured 1-D Grid Generator395
- 12.3 Structured 2-D Grid Generators396
- 12.4 Structured to Unstructured Grid Converter396
- 12.5 Quasi 1-D Euler Solver396
- 12.6 Structured 2-D Euler Solver398
- 12.7 Unstructured 2-D Euler Solver400
- Bibliography400
- Appendix A401
- A.1 Governing Equations in Differential Form401
- A.2 Mathematical Character of the Governing Equations407
- A.3 Navier-Stokes Equations in Rotating Frame of Reference411
- A.4 Navier-Stokes Equations Formulated for Moving Grids414
- A.5 Thin Shear Layer Approximation416
- A.6 Parabolised Navier-Stokes Equations418
- A.7 Convective Flux Jacobian419
- A.8 Viscous Flux Jacobian421
- A.9 Transformation from Conservative to Characteristic Variables424
- A.10 GMRES Algorithm427
- A.11 Tensor Notation431
- Bibliography432
- Index435
Computational Fluid Dynamics: Principles and Applications