Fletcher C.A.J. Computational Techniques for Fluid Dynamics 2: Specific Techniques for Different Flow Categories

Springer-Verlag, 1998. 496 p.
SBN 3-540-18759-6 Springer-Verlag Berlin Heidelberg New York
SBN 0-387-18759-6 Springer-Verlag New York Berlin HeidelbergThe purpose of this textbook is to provide senior undergraduate and postgraduate engineers, scientists and applied mathematicians with the specific techniques, and the framework to develop skills in using the techniques, that have proven effective in the various brances of computational fluid dynamicsFluid Dynamics: The Governing Equations
Physical Properties of Fluids
Equations of Motion
Continuity Equation
Momentum Equations: Inviscid Flow
Momentum Equations: Viscous Flow
Energy Equation
Dynamic Similarity
Useful Simplifications
Incompressible, Inviscid Flow
Incompressible Boundary Layer Flow
Laminar Boundary Layer Flow
Turbulent Boundary Layer Flow
Boundary Layer Separation
Incompressible, Viscous Flow
Laminar Flow
Turbulent Flow
Compressible Flow
Inviscid Compressible Flow
Compressible Boundary Layer Flow
Compressible Viscous Flow
Boundary Conditions for Compressible Viscous Flow
Closure
Problems
Generalised Curvilinear Coordinates
Transformation Relationships
Generalised Coordinates
Metric Tensor and the Physical Features of the Transformation
Restriction to Orthogonal and Conformal Coordinates
Evaluation of the Transformation Parameters
Centred-Difference Formulae
Finite Element Evaluation
Additional Errors Associated with the Use of Generalised Coordinates Generalised Coordinate Structure of Typical Equations
General First-Order Partial Differential Equation
General Second-Order Partial Differential Equation
Equations Governing Fluid Flow
Numerical Implementation of Generalised Coordinates
Lagen: Generalised Coordinate Laplace Equation
Closure
Problems
Grid Generation
Physical Aspects
Simply-Connected Regions
Multiply-Connected Regions
Grid Generation by Partial Differential Equation Solution
Conformal Mapping: General Considerations
Sequential Conformal Mapping
One-step Conformal Mapping
Orthogonal Grid Generation
Near-Orthogonal Grids
Solution of Elliptic Partial Differential Equations
Grid Generation by Algebraic Mapping
One-Dimensional Stretching Functions
Two Boundary Technique
Multisurface Method
Transfinite Interpolation
Numerical Implementation of Algebraic Mapping
Algem: Grid Generation for a Streamlined Body
Closure
Problems
Inviscid Flow
Panel Method
Panel Method for Inviscid Incompressible Flow
Panel: Numerical Implementation
Connection with the Boundary Element Method
Lifting Aerofoil Problem
Higher-Order Panel Methods and the Extension to Three Dimensions
Panel Method for Inviscid, Compressible Flow
Supersonic Inviscid Flow
Preliminary Considerations
MacCormack's Predictor-Corrector Scheme
Shock: Propagating Shock Wave Computation Inclined Cone Problem
Moretti 2-Scheme
Computation of Strong Shocks
FCT: Propagating Shockwave by an FCT Algorithm
mplicit Schemes for the Euler Equations
Multigrid for Euler Equations
Transonic Inviscid Flow
General Considerations
Transonic Small Disturbance Equation
Full Potential Equation
Transonic Inviscid Flow: Generalised Coordinates
Solution of the Algebraic Equations
Non-isentropic Potential Formulation
Full-Potential Equation, Further Comments
Closure
Problems
Boundary Layer Flow
Simple Boundary Layer Flow
Implicit Scheme
Lambl: Laminar Boundary Layer Flow
Keller Box Scheme
Complex Boundary Layer Flow
Change of Variables
Levy-Lees Transformation
Davis Coupled Scheme
Dorodnitsyn Boundary Layer Formulation
Dorodnitsyn Finite Element Method
Dorod: Turbulent Boundary Layer Flow
Dorodnitsyn Spectral Method
Three-Dimensional Boundary Layer Flow
Subcharacteristic Behaviour
Generalised Coordinates
Implicit Split Marching Algorithm
Closure
Problems
Flows Governed by Reduced Navier-Stokes EquationsOrder-of-Magnitude Analysis
Fourier Analysis for Qualitative Solution Behaviour
Qualitative Solution Behaviour of the Reduced Navier-Stokes Equations
Thred: Thermal Entry Problem
Internal Flow
nternal Swirling Flow
Flow in a Straight Rectangular Duct
Flow in a Curved Rectangular Duct
External Flow
Supersonic Flow
Subsonic Flow
Incompressible Flow
Viscous, Inviscid Interactions
Quasi-Simultaneous Interaction Method
Semi-Inverse Interaction Method
Viscous, Inviscid Interaction Using the Euler Equations
Closure
Problems
Incompressible Viscous Flow
Primitive Variables: Unsteady Flow
Staggered Grid
MAC Formulation
Implementation of Boundary Conditions
Developments of the MAC Method
Higher-Order Upwinding Differencing
Spectral Methods
Primitive Variables: Steady Flow
Artificial Compressibility
Auxiliary Potential Function
Simple Formulations
Finite Element Formulation
Vorticity, Stream Function Variables
Finite Difference Formulations
Boundary Condition Implementation
Group Finite Element Formulation
Pressure Solution
Vorticity Formulations for Three-Dimensional Flows
Vorticity, Vector Potential Formulation
Vorticity, Velocity Formulation
Closure
Problems
Compressible Viscous Flow
Physical Simplifications
Eddy Viscosity Turbulence Modelling
Constant Total Enthalpy Flow
Thin Layer Approximation
Explicit Schemes
Explicit MacCormack Scheme
Runge-Kutta Schemes
Implicit Schemes
Implicit MacCormack Scheme
Beam and Warming Scheme
Group Finite Element Method
Approximate LU Factorisation
Generalised Coordinates
Steger Thin Layer Formulation
Approximate Factorisation Finite Element Method
Numerical Dissipation
High Reynolds Number Flows
Shock Waves
Closure
ProblemsSubject Index
Con tens of Computational Techniques for Fluid Dynamics
Fundamental and General Techniques