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.

As indicated in Vol. 1, the purpose of this two-volume textbook is to pro­ vide students of engineering, science and applied mathematics with the spe­ cific techniques, and the framework to develop skill in using them, that have proven effective in the various branches of computational fluid dy­ namics Volume 1 describes both fundamental and general techniques that are relevant to all branches of fluid flow. This volume contains specific tech­ niques applicable to the different categories of engineering flow behaviour, many of which are also appropriate to convective heat transfer. The contents of Vol. 2 are suitable for specialised graduate courses in the engineering computational fluid dynamics (CFD) area and are also aimed at the established research worker or practitioner who has already gained some fundamental CFD background. It is assumed that the reader is famil­ iar with the contents of Vol. 1. The contents of Vol. 2 are arranged in the following way: Chapter 11 de­ velops and discusses the equations governing fluid flow and introduces the simpler flow categories for which specific computational techniques are considered in Chaps. 14-18. Most practical problems involve computational domain boundaries that do not conveniently coincide with coordinate lines. Consequently, in Chap. 12 the governing equations are expressed in generalised curvilinear coordinates for use in arbitrary computational domains. The corresponding problem of generating an interior grid is considered in Chap. 13.