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-Kiic-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 Equations
4．2-2 The Grid Spacing
4．2-3 The Interface Conductmty
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
……
6 CALCULATION OF THE FLOW FIELD
7 FINISHING TOUCHES
8 SPECIAL TOPICS
9 ILLUSTRATIVE APPLICATIONS
Nomenclature
References
Index
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-Kiic-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 Equations
4．2-2 The Grid Spacing
4．2-3 The Interface Conductmty
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
……
6 CALCULATION OF THE FLOW FIELD
7 FINISHING TOUCHES
8 SPECIAL TOPICS
9 ILLUSTRATIVE APPLICATIONS
Nomenclature
References
Index