11. Fluid Dynamics: The Governing Equations.- 11.1 Physical Properties of Fluids.- 11.2 Equations of Motion.- 11.2.1 Continuity Equation.- 11.2.2 Momentum Equations: Inviscid Flow.- 11.2.3 Momentum Equations: Viscous Flow.- 11.2.4 Energy Equation.- 11.2.5 Dynamic Similarity.- 11.2.6 Useful Simplifications.- 11.3 Incompressible, Inviscid Flow.- 11.4 Incompressible Boundary Layer Flow.- 11.4.1 Laminar Boundary Layer Flow.- 11.4.2 Turbulent Boundary Layer Flow.- 11.4.3 Boundary Layer Separation.- 11.5 Incompressible, Viscous Flow.- 11.5.1 Laminar Flow.- 11.5.2 Turbulent Flow.- 11.6 Compressible Flow.- 11.6.1 Inviscid Compressible Flow.- 11.6.2 Compressible Boundary Layer Flow.- 11.6.3 Compressible Viscous Flow.- 11.6.4 Boundary Conditions for Compressible Viscous Flow.- 11.7 Closure.- 11.8 Problems.- 12. Generalised Curvilinear Coordinates.- 12.1 Transformation Relationships.- 12.1.1 Generalised Coordinates.- 12.1.2 Metric Tensor and the Physical Features of the Transformation.- 12.1.3 Restriction to Orthogonal and Conformal Coordinates.- 12.2 Evaluation of the Transformation Parameters.- 12.2.1 Centred-Difference Formulae.- 12.2.2 Finite Element Evaluation.- 12.2.3 Additional Errors Associated with the Use of Generalised Coordinates.- 12.3 Generalised Coordinate Structure of Typical Equations.- 12.3.1 General First-Order Partial Differential Equation.- 12.3.2 General Second-Order Partial Differential Equation.- 12.3.3 Equations Governing Fluid Flow.- 12.4 Numerical Implementation of Generalised Coordinates.- 12.4.1 LAGEN: Generalised Coordinate Laplace Equation.- 12.5 Closure.- 12.6 Problems.- 13. Grid Generation.- 13.1 Physical Aspects.- 13.1.1 Simply-Connected Regions.- 13.1.2 Multiply-Connected Regions.- 13.2 Grid Generation by Partial Differential Equation Solution.- 13.2.1 Conformal Mapping: General Considerations.- 13.2.3 Sequential Conformal Mapping.- 13.2.3 One-step Conformal Mapping.- 13.2.4 Orthogonal Grid Generation.- 13.2.5 Near-Orthogonal Grids.- 13.2.6 Solution of Elliptic Partial Differential Equations.- 13.3 Grid Generation by Algebraic Mapping.- 13.3.1 One-Dimensional Stretching Functions.- 13.3.2 Two Boundary Technique.- 13.3.3 Multisurface Method.- 13.3.4 Transfinite Interpolation.- 13.4 Numerical Implementation of Algebraic Mapping.- 13.4.1 ALGEM: Grid Generation for a Streamlined Body.- 13.5 Closure.- 13.6 Problems.- 14. Inviscid Flow.- 14.1 Panel Method.- 14.1.1 Panel Method for Inviscid Incompressible Flow.- 14.1.2 PANEL: Numerical Implementation.- 14.1.3 Connection with the Boundary Element Method.- 14.1.4 Lifting Aerofoil Problem.- 14.1.5 Higher-Order Panel Methods and the Extension to Three Dimensions.- 14.1.6 Panel Method for Inviscid, Compressible Flow.- 14.2 Supersonic Inviscid Flow.- 14.2.1 Preliminary Considerations.- 14.2.2 MacCormack's Predictor-Corrector Scheme.- 14.2.3 SHOCK: Propagating Shock Wave Computation.- 14.2.4 Inclined Cone Problem.- 14.2.5 Moretti ?-Scheme.- 14.2.6 Computation of Strong Shocks.- 14.2.7 FCT: Propagating Shockwave by an FCT Algorithm.- 14.2.8 Implicit Schemes for the Euler Equations.- 14.2.9 Multigrid for Euler Equations.- 14.3 Transonic Inviscid Flow.- 14.3.1 General Considerations.- 14.3.2 Transonic Small Disturbance Equation.- 14.3.3 Full Potential Equation.- 14.3.4 Transonic Inviscid Flow: Generalised Coordinates.- 14.3.5 Solution of the Algebraic Equations.- 14.3.6 Non-isentropic Potential Formulation.- 14.3.7 Full-Potential Equation, Further Comments.- 14.4 Closure.- 14.5 Problems.- 15. Boundary Layer Flow.- 15.1 Simple Boundary Layer Flow.- 15.1.1 Implicit Scheme.- 15.1.2 LAMBL: Laminar Boundary Layer Flow.- 15.1.3 Keller Box Scheme.- 15.2 Complex Boundary Layer Flow.- 15.2.1 Change of Variables.- 15.2.2 Levy-Lees Transformation.- 15.2.3 Davis Coupled Scheme.- 15.3 Dorodnitsyn Boundary Layer Formulation.- 15.3.1 Dorodnitsyn Finite Element Method.- 15.3.2 DOROD: Turbulent Boundary Layer Flow.- 15.3.3 Dorodnitsyn Spectral Method.- 15.4 Three-Dimensional Boundary Layer Flow.- 15.4.1 Subcharacteristic Behaviour.- 15.4.2 Generalised Coordinates.- 15.4.3 Implicit Split Marching Algorithm.- 15.5 Closure.- 15.6 Problems.- 16. Flows Governed by Reduced Navier-Stokes Equations.- 16.1 Introduction.- 16.1.1 Order-of-Magnitude Analysis.- 16.1.2 Fourier Analysis for Qualitative Solution Behaviour.- 16.1.3 Qualitative Solution Behaviour of the Reduced Navier-Stokes Equations.- 16.1.4 THRED: Thermal Entry Problem.- 16.2 Internal Flow.- 16.2.1 Internal Swirling Flow.- 16.2.2 Flow in a Straight Rectangular Duct.- 16.2.3 Flow in a Curved Rectangular Duct.- 16.3 External Flow.- 16.3.1 Supersonic Flow.- 16.3.2 Subsonic Flow.- 16.3.3 Incompressible Flow.- 16.3.4 Viscous, Inviscid Interactions.- 16.3.5 Quasi-Simultaneous Interaction Method.- 16.3.6 Semi-Inverse Interaction Method.- 16.3.7 Viscous, Inviscid Interaction Using the Euler Equations.- 16.4 Closure.- 16.5 Problems.- 17. Incompressible Viscous Flow.- 17.1 Primitive Variables: Unsteady Flow.- 17.1.1 Staggered Grid.- 17.1.2 MAC Formulation.- 17.1.3 Implementation of Boundary Conditions.- 17.1.4 Developments of the MAC Method.- 17.1.5 Higher-Order Upwinding Differencing.- 17.1.6 Spectral Methods.- 17.2 Primitive Variables: Steady Flow.- 17.2.1 Artificial Compressibility.- 17.2.2 Auxiliary Potential Function.- 17.2.3 SIMPLE Formulations.- 17.2.4 Finite Element Formulation.- 17.3 Vorticity, Stream Function Variables.- 17.3.1 Finite Difference Formulations.- 17.3.2 Boundary Condition Implementation.- 17.3.3 Group Finite Element Formulation.- 17.3.4 Pressure Solution.- 17.4 Vorticity Formulations for Three-Dimensional Flows.- 17.4.1 Vorticity, Vector Potential Formulation.- 17.4.2 Vorticity, Velocity Formulation.- 17.5 Closure.- 17.6 Problems.- 18. Compressible Viscous Flow.- 18.1 Physical Simplifications.- 18.1.1 Eddy Viscosity Turbulence Modelling.- 18.1.2 Constant Total Enthalpy Flow.- 18.1.3 Thin Layer Approximation.- 18.2 Explicit Schemes.- 18.2.1 Explicit MacCormack Scheme.- 18.2.2 Runge-Kutta Schemes.- 18.3 Implicit Schemes.- 18.3.1 Implicit MacCormack Scheme.- 18.3.2 Beam and Warming Scheme.- 18.3.3 Group Finite Element Method.- 18.3.4 Approximate LU Factorisation.- 18.4 Generalised Coordinates.- 18.4.1 Steger Thin Layer Formulation.- 18.4.2 Approximate Factorisation Finite Element Method.- 18.5 Numerical Dissipation.- 18.5.1 High Reynolds Number Flows.- 18.5.2 Shock Waves.- 18.6 Closure.- 18.7 Problems.- References.- Contens of Computational Techniques for Fluid Dynamics 1 Fundamental and General Techniques.