●Preface
1 INTRODUCTION
1.1 Scope of the Book
1.2 Methods of Prediction
1.2-1 Experimental Investigation
1.2-2 Theoretical Calculation
1.2-3 Advantages of a Theoretical Calculation
1.2-4 Disadvantages of a Theoretical Calculation
1.2-5 Choice of Prediction Method
1.3 Outline of the Book
2 MATHEMATICAL DESCRIPTION OF PHYSICAL PHENOMENA
2.1 Governing Differential Equations
2.1-1 Meaning of a Differential Equation
2.1-2 Conservation of a Chemical Species
2.1-3 The Energy Equation
2.1-4 A Momentum Equation
2.1-5 The Time-Averaged Equations for Turbulent Flow
2.1-6 The Turbulence-Kinetic-Energy Equation
2.1-7 The General Differential Equation
2.2 Nature of Coordinates
2.2-1 Independent Variables
2.2-2 Proper Choice of Coordinates
2.2-3 One-Way and Two-Way Coordinates
Problems
3 DISCRETIZATION METHODS
3.1 The Nature of Numerical Methods
3.1-1 The Task
3.1-2 The Discretization Concept
3.1-3 The Structure of the Discretization Equation
3.2 Methods of Deriving the Discretization Equations
3.2-1 Taylor-Series Formulation
3.2-2 Variational Formulation
3.2-3 Method of Weighted Residuals
3.2-4 Control-Volume Formulation
3.3 An Illustrative Example
3.4 The Four Basic Rules
3.5 Closure
Problems
4 HEAT CONDUCTION
4.1 Objectives of the Chapter
4.2 Steady One-dimensional Conduction
4.2-1 The Basic Eguations
4.2-2 The Grid Spacing
4.2-3 The Interface Conductivity
4.2-4 Nonlinearity
4.2-5 Source-Term Linearization
4.2-6 Boundary Conditions
4.2-7 Solution of the Linear Algebraic Equations
4.3 Unsteady One-dimensional Conduction
4.3-1 The General Discretization Equation
4.3-2 Explicit,Crank-Nicolson,and Fully Implicit Schemes
4.3-3 The Fully Implicit Discretization Equation
4.4 Two- and Three-dimensional Situations
4.4-1 Discretization Equation for Two Dimensions
4.4-2 Discretization Equation for Three Dimensions
4.4-3 Solution of the Algebraic Equations
4.5 Overrelaxation and Underrelaxation
4.6 Some Geometric Considerations
4.6-1 Location of the Control-Volume Faces
4.6-2 Other Coordinate Systems
4.7 Closure
Problems
5 CONVECTION AND DIFFUSION
5.1 The Task
5.2 Steady One-dimensional Convection and Diffusion
5.2-1 A Preliminary Derivation
5.2-2 The Upwind Scheme
5.2-3 The Exact Solution
5.2-4 The Exponential Scheme
5.2-5 The Hybrid Scheme
5.2-6 The Power-Law Scheme
5.2-7 A Generalized Formulation
5.2-8 Consequences of the Various Schemes
5.3 Discretization Equation for Two Dimensions
5.3-1 Details of the Derivation
5.3-2 The Final Discretization Equation
5.4 Discretization Equation for Three Dimensions
5.5 A One-Way Space Coordinate
5.5-1 What Makes a Space Coordinate One-Way
5.5-2 The Outflow Boundary Condition
5.6 False Diffusion
5.6-1 The Common View of False Diffusion
5.6-2 The Proper View of False Diffusion
5.7 Closure
Problems
6 CALCULATION OF THE FLOW FIELD
6.1 Need for a Special Procedure
6.1-1 The Main Difficulty
6.1-2 Vorticity-based Methods
6.2 Some Related Difficulties
6.2-1 Representation of the Pressure-Gradient Term
6.2-2 Representation of the Continuity Equation
6.3 A Remedy:The Staggered Grid
6.4 The Momentum Equations
6.5 The Pressure and Velocity Corrections
6.6 The Pressure-Correction Equation
6.7 The SIMPLE Algorithm
6.7-1 Sequence of Operations
6.7-2 Discussion of the Pressure-Correction Equation
6.7-3 Boundary Conditions for the Pressure-Correction Equation
6.7-4 The Relative Nature of Pressure
6.8 A Revised Algorithm:SIMPLER
6.8-1 Motivation
6.8-2 The Pressure Equation
6.8-3 The SIMPLER Algorithm
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