Notes on Computational Fluid Dynamics: General Principles

Preface
Symbols
1 Introduction
 1.1 Solution overview
2 Fluid Dynamics
 2.1 Pressure
 2.2 Velocity
 2.3 Flow through a surface
 2.4 Conservation of mass
 2.5 Time derivatives
 2.6 Forces at a surface
 2.7 Conservation of momentum
 2.8 Flow in a volume
 2.9 Conservation and boundedness
 2.10 Fluid deformation
 2.11 Vorticity
 2.12 Newtonian fluid
 2.13 Incompressible flow
 2.14 Diffusion
 2.15 Conservation of energy
 2.16 Temperature
 2.17 Internal energy
 2.18 Heat capacity
 2.19 Energy and temperature
 2.20 Natural convection
 2.21 Scale similarity
 2.22 Region of influence
 2.23 Summary of equations
 2.24 Summary of tensor algebra
 2.25 Vector identities
3 Numerical Method
 3.1 The finite volume concept
 3.2 Computational mesh
 3.3 Finite volume mesh
 3.4 Equation discretisation
 3.5 Matrix construction
 3.6 Overview of discretisation
 3.7 Laplacian discretisation
 3.8 Surface normal gradient
 3.9 Advection discretisation
 3.10 Upwind scheme
 3.11 Limited advection schemes
 3.12 Useful TVD schemes
 3.13 Limiting multiple components
 3.14 Linear upwind scheme
 3.15 Gradient discretisation
 3.16 Gradient limiting
 3.17 Time discretisation
 3.18 Second order time schemes
 3.19 Calculated derivatives
 3.20 Other terms
 3.21 Terms which change sign
 3.22 Bounded advection discretisation
 3.23 Recommended discretisation schemes
 3.24 Example of building a matrix equation
4 Boundary Conditions
 4.1 Boundary mesh
 4.2 Fixed value and fixed gradient
 4.3 Fundamentals of boundary conditions
 4.4 Wall boundaries
 4.5 Inlets and outlets
 4.6 Free (entrainment) boundaries
 4.7 Total pressure condition
 4.8 Numerical framework
 4.9 Mixed fixed value/gradient
 4.10 Mixed inlet-outlet condition
 4.11 Transform condition
 4.12 Symmetry condition
 4.13 Axisymmetric (wedge) condition
 4.14 Direction mixed condition
 4.15 Inlet-outlet-velocity condition
 4.16 Blended freestream condition
 4.17 External wall heat flux
 4.18 Recommended boundary conditions
5 Algorithms and Solvers
 5.1 Structure of matrices
 5.2 Gauss-Seidel method
 5.3 Convergence
 5.4 Residual
 5.5 Diagonal dominance
 5.6 Under-relaxation
 5.7 Iterative solution
 5.8 Accelerating convergence
 5.9 Systems of equations
 5.10 Pressure-velocity coupling
 5.11 Boundary fluxes
 5.12 Steady-state solution
 5.13 Steady-state convergence
 5.14 Descent methods
 5.15 Conjugate gradient method
 5.16 Preconditioning and asymmetry
 5.17 Multi-grid method
 5.18 GAMG method
 5.19 Transient solution
 5.20 Transient solution controls
 5.21 The PIMPLE algorithm
 5.22 Solving for energy
 5.23 Summary of algorithms and solvers
6 Introduction to Turbulence
 6.1 Reynolds experiment
 6.2 A picture of turbulence
 6.3 Vorticity transport
 6.4 Boundary layers
 6.5 Boundary layer separation
 6.6 Scales of turbulence
 6.7 Energy cascade
 6.8 The cost of simulating turbulence
 6.9 Reynolds-averaged simulation
 6.10 The nature of viscosity
 6.11 Turbulent mixing
 6.12 Mixing length
 6.13 Turbulent kinetic energy
 6.14 Turbulent dissipation rate
 6.15 Summary of turbulence
7 Reynolds-Averaged Turbulence Modelling
 7.1 The k-epsilon turbulence model
 7.2 Initialisation of the k-epsilon model
 7.3 Inlet turbulence
 7.4 Turbulent boundary layers
 7.5 Wall functions
 7.6 Alternative wall functions
 7.7 Turbulence near walls
 7.8 Resolving the viscous sub-layer
 7.9 Low-Re k-epsilon models
 7.10 Specific dissipation rate
 7.11 Enhancements to the k-omega model
 7.12 Heat transfer in turbulent flow
 7.13 Thermal boundary layers
 7.14 Thermal wall functions
 7.15 Summary of turbulence modelling
8 Sample Problems
 8.1 External flows
 8.2 Aspect ratio
 8.3 Block-structured meshes
 8.4 Flow around a cylinder
 8.5 Unstructured hex-dominant meshes
 8.6 Automotive aerodynamics
 8.7 Nonuniform inlet velocity
 8.8 Venturi tube
 8.9 Heating a room
 8.10 Building a CFD simulation
Index