Preface
Acknowledgements
1 Introduction
1.1 What is CFD?
1.2 How does a CFD code work?
1.3 Problem solving with CFD
1.4 Scope of this book
2 Conservation laws of fluid motion and boundary conditions
2.1 Governing equations of fluid flow and heat transfer
2.1.1 Mass conservation in three dimensions
2.1.2 Rates of change following a fluid particle and for a fluid element
2.1.3 Momentum equation in three dimensions
2.1.4 Energy equation in three dimensions
2.2 Equations of state
2.3 Navier-Stokes equations for a Newtonian fluid
2.4 Conservative form of the governing equations of fluid flow
2.5 Differential and integral forms of the general transport equations
2.6 Classification of physical behaviours
2.7 The role of characteristics in hyperbolic equations
2.8 Classification method for simple PDEs
2.9 Classification of fluid flow equations
2.10 Auxiliary conditions for viscous fluid flow equations
2.11 Problems in transonic and supersonic compressible flows
2.12 Summary
3 Turbulence and its modelling
3.1 What is turbulence?
3.2 Transition from laminar to turbulent flow
3.3 Descriptors of turbulent flow
3.4 Characteristics of simple turbulent flows
3.4.1 Free turbulent flows
3.4.2 Flat plate boundary layer and pipe flow
3.4.3 Summary
3.5 The effect of turbulent fluctuations on properties of the mean flow
3.6 Turbulent flow calculations
3.7 Reynolds-averaged Navier-Stokes equations and classical turbulence models
3.7.1 Mixing length model
3.7.2 The k-ε model
3.7.3 Reynolds stress equation models
3.7.4 Advanced turbulence models
3.7.5 Closing remarks-RANS turbulence models
3.8 Large eddy simulation
3.8.1 Spacial filtering of unsteady Navier-Stokes equations
3.8.2 Smagorinksy-Lilly SGS model
3.8.3 Higher-order SGS models
3.8.4 Advanced SGS models
3.8.5 Initial and boundary conditions for LES
3.8.6 LES applications in flows with complex geometry
3.8.7 General comments on performance of LES
3.9 Direct numerical simulation
3.9.1 Numerical issues in DNS
3.9.2 Some achievements of DNS
3.10 Summary
4 The finite volume method for diffusion problems
4.1 Introduction
4.2 Finite volume method for one-dimensional steady state diffusion
4.3 Worked examples: one-dimensional steady state diffusion
4.4 Finite volume method for two-dimensional diffusion problems
4.5 Finite volume method for three-dimensional diffusion problems
4.6 Summary
5 The finite volume method for convection-diffusion problems
5.1 Introduction
5.2 Steady one-dimensional convection and diffusion
5.3 The central differencing scheme
5.4 Properties of discretisation schemes
5.4.1 Conservativeness
5.4.2 Boundedness
5.4.3 Transportiveness
5.5 Assessment of the central differencing scheme for convection-diffusion problems
5.6 The upwind differencing scheme
5.6.1 Assessment of the upwind differencing scheme
5.7 The hybrid differencing scheme
5.7.1 Assessment of the hybrid differencing scheme
5.7.2 Hybrid differencing scheme for multi-dimensional convection-diffusion
5.8 The power-law scheme
5.9 Higher-order differencing schemes for convection-diffusion problems
5.9.1 Quadratic upwind differencing scheme: the QUICK scheme
5.9.2 Assessment of the QUICK scheme
5.9.3 Stability problems of the QUICK scheme and remedies
5.9.4 General comments on the QUICK differencing scheme
5.10 TVD schemes
5.10.1 Generalisation of upwind-biased discretisation schemes
5.10.2 Total variation and TVD schemes
5.10.3 Criteria for TVD schemes
5.10.4 Flux limiter functions
5.10.5 Implementation of TVD schemes
5.10.6 Evaluation of TVD schemes
5.11 Summary
6 Solution algorithms for pressure-velocity coupling in ste
