From the Book - Regular Print - Second edition.
2 Governing Equations 5 --
2.1 Flow and its Mathematical Description 5 --
2.2 Conservation Laws 8 --
2.3 Viscous Stresses 13 --
2.4 Complete System of the Navier-Stokes Equations 16 --
3 Principles of Solution of the Governing Equations 29 --
3.1 Spatial Discretisation 32 --
3.2 Temporal Discretisation 45 --
3.3 Turbulence Modelling 53 --
3.4 Initial and Boundary Conditions 56 --
4 Structured Finite Volume Schemes 77 --
4.1 Geometrical Quantities of a Control Volume 81 --
4.2 General Discretisation Methodologies 85 --
4.3 Discretisation of the Convective Fluxes 95 --
4.4 Discretisation of the Viscous Fluxes 118 --
5 Unstructured Finite Volume Schemes 131 --
5.1 Geometrical Quantities of a Control Volume 136 --
5.2 General Discretisation Methodologies 141 --
5.3 Discretisation of the Convective Fluxes 153 --
5.4 Discretisation of the Viscous Fluxes 172 --
6 Temporal Discretisation 183 --
6.1 Explicit Time-Stepping Schemes 184 --
6.2 Implicit Time-Stepping Schemes 192 --
6.3 Methodologies for Unsteady Flows 214 --
7 Turbulence Modelling 227 --
7.1 Basic Equations of Turbulence 230 --
7.2 First-Order Closures 240 --
7.3 Large-Eddy Simulation 250 --
8 Boundary Conditions 271 --
8.1 Concept of Dummy Cells 272 --
8.4 Inlet/Outlet Boundary 287 --
8.5 Injection Boundary 289 --
8.6 Symmetry Plane 290 --
8.7 Coordinate Cut 291 --
8.8 Periodic Boundaries 292 --
8.9 Interface Between Grid Blocks 295 --
8.10 Flow Gradients at Boundaries of Unstructured Grids 298 --
9 Acceleration Techniques 303 --
9.1 Local Time-Stepping 304 --
9.2 Enthalpy Damping 305 --
9.3 Residual Smoothing 306 --
9.5 Preconditioning for Low Mach Numbers 327 --
10 Consistency, Accuracy and Stability 351 --
10.1 Consistency Requirements 352 --
10.2 Accuracy of Discretisation 353 --
10.3 Von Neumann Stability Analysis 354 --
11 Principles of Grid Generation 373 --
11.1 Structured Grids 376 --
11.2 Unstructured Grids 388 --
12 Description of the Source Codes 415 --
12.1 Programs for Stability Analysis 417 --
12.2 Structured 1-D Grid Generator 417 --
12.3 Structured 2-D Grid Generators 418 --
12.4 Structured to Unstructured Grid Converter 419 --
12.5 Quasi 1-D Euler Solver 419 --
12.6 Structured 2-D Euler/Navier-Stokes Solver 420 --
12.7 Unstructured 2-D Euler/Navier-Stokes Solver 421 --
12.8 Visualisation Tool 423 --
A.1 Governing Equations in Differential Form 427 --
A.2 Quasilinear Form of the Euler Equations 433 --
A.3 Mathematical Character of the Governing Equations 434 --
A.4 Navier-Stokes Equations in Rotating Frame of Reference 438 --
A.5 Navier-Stokes Equations Formulated for Moving Grids 441 --
A.6 Thin Shear Layer Approximation 445 --
A.7 Parabolised Navier-Stokes Equations 447 --
A.8 Axisymmetric Form of the Navier-Stokes Equations 448 --
A.9 Convective Flux Jacobian 450 --
A.10 Viscous Flux Jacobian 452 --
A.11 Transformation from Conservative to Characteristic Variables 455 --
A.12 GMRES Algorithm 458 --
A.13 Tensor Notation 462.