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```Contents
Nomenclature page xiii
Preface xvii
1. Introduction
1.1 CFD Activity
1.2 Transport Equations
1.3 Numerical versus Analytical Solutions
1.5 A Note on Navier--Stokes Equations
1.6 Outline of the Book
Exercises
2. 1D Heat Conduction
2.1 Introduction
2.2 1D Conduction Equation
2.3 Grid Layout
2.4 Discretisation
2.4.1 TSE Method
2.4.2 IOCV Method
2.5 Stability and Convergence
2.5.1 Explicit Procedure ? = 0
2.5.2 Partially Implicit Procedure 0 < ? < 1
2.5.3 Implicit Procedure ? = 1
2.6 Making Choices
2.7 Dealing with Nonlinearities
2.7.1 Nonlinear Sources
2.7.2 Nonlinear Coefficients
2.7.3 Boundary Conditions
2.7.4 Underrelaxation
2.8 Methods of Solution
2.8.1 Gauss--Seidel Method
2.8.2 Tridiagonal Matrix Algorithm
2.8.3 Application
2.9 Problems from Related Fields
Exercises
3. 1D Conduction--Convection
3.1 Introduction
3.2 Exact Solution
3.3 Discretisation
3.4 Upwind Difference Scheme
3.5 Comparison of CDS, UDS, and Exact Solution
3.6 Numerical False Diffusion
3.7 Hybrid and Power-Law Schemes
3.8 Total Variation Diminishing Scheme
3.9 Stability of the Unsteady Equation
3.9.1 Exact Solution
3.9.2 Explicit Finite-Difference Form
3.9.3 Implicit Finite-Difference Form
Exercises
4. 2D Boundary Layers
4.1 Governing Equations
4.3 Transformation to (x, ?) Coordinates
4.4 Discretisation
4.5 Determination of ?, y, and r
4.6 Boundary Conditions
4.6.1 Symmetry
4.6.2 Wall
4.6.3 Free Stream
4.7 Source Terms
4.7.2 Q''' and Rk
4.8 Treatment of Turbulent Flows
4.8.1 Mixing Length Model
4.8.2 Model
4.8.3 Free-shear Flows
4.9 Overall Procedure
4.9.1 Calculation Sequence
4.9.2 Initial Conditions
4.9.3 Choice of Step Size and Iterations
4.10 Applications
Exercises
5. 2D Convection -- Cartesian Grids
5.1 Introduction
5.1.2 Solution Strategy
5.2 SIMPLE -- Collocated Grids
5.2.1 Main Idea
5.2.2 Discretisation
5.2.3 Pressure-Correction Equation
5.2.4 Further Simplification
5.2.5 Overall Calculation Procedure
5.3 Method of Solution
5.3.1 Iterative Solvers
5.3.2 Evaluation of Residuals
5.3.3 Underrelaxation
5.3.4 Boundary Conditions for
5.3.5 Boundary Condition for p_m
5.3.6 Node Tagging
5.4 Treatment of Turbulent Flows
5.4.1 LRE Model
5.4.2 HRE Model
5.5 Notion of Smoothing Pressure Correction
5.6 Applications
Exercises
6. 2D Convection -- Complex Domains
6.1 Introduction
6.1.1 Curvilinear Grids
6.1.2 Unstructured Grids
6.2 Curvilinear Grids
6.2.1 Coordinate Transformation
6.2.2 Transport Equation
6.2.3 Interpretation of Terms
6.2.4 Discretisation
6.2.5 Pressure-Correction Equation
6.2.6 Overall Calculation Procedure
6.2.7 Node Tagging and Boundary Conditions
6.3 Unstructured Meshes
6.3.2 Gauss's Divergence Theorem
6.3.3 Construction of a Line Structure
6.3.4 Convective Transport
6.3.5 Diffusion Transport
6.3.6 Interim Discretised Equation
6.3.7 Interpolation of _ at P2, E2, a, and b
6.3.8 Final Discretised Equation
6.3.10 Boundary Conditions
6.3.11 Pressure-Correction Equation
6.3.12 Method of Solution
6.3.13 Overall Calculation Procedure
6.4 Applications
6.5 Closure
Exercises
7. Phase Change
7.1 Introduction
7.2 1D Problems for Pure Substances
7.2.1 Exact Solution
7.2.2 Simple Numerical Solution
7.2.3 Numerical Solution Using TDMA
7.2.4 Accurate Solutions on a Coarse Grid
7.3 1D Problems for Impure Substances
Exercises
8. Numerical Grid Generation
8.1 Introduction
8.2 Algebraic Grid Generation
8.2.1 1D Domains
8.2.2 2D Domains
8.3 Differential Grid Generation
8.3.1 1D Domains
8.3.2 2D Domains
8.3.3 Inversion of Determinant Equations
8.4 Sorenson's Method
8.4.1 Main Specifications
8.4.2 Stretching Functions
8.4.3 Discretisation
8.4.4 Solution Procedure
8.4.5 Applications
8.5 Unstructured Mesh Generation
8.5.2 Domains with (i , j ) Structure
8.5.3 Automatic Grid Generation
Exercises
9. Convergence Enhancement
9.1 Convergence Rate
9.2 Block Correction
9.3 Method of Two-Lines
9.4 Stone's Method
9.5 Applications
Exercises
Appendix A. Derivation of Transport Equations
Appendix B. 1D Conduction Code
Appendix C. 2D Cartesian Code
Bibliography
Index
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Library of Congress Subject Headings for this publication:

Fluid dynamics -- Mathematics -- Textbooks.
Numerical analysis -- Textbooks.