Page 11 - Computational Fluid Dynamics for Engineers

X Contents

2.7 Boundary Conditions 70
References 72
Problems 73

3. Turbulence Models 81
3.1 Introduction 81
3.2 Zero-Equation Models 83
3.2.1 Cebeci-Smith Model 83
3.2.2 Baldwin-Lomax Model 85
3.3 One-Equation Models 87
3.4 Two-Equation Models 88
3.5 Initial Conditions 90
References 93

4. Numerical Methods for Model Parabolic
and Elliptic Equations 95
4.1 Introduction 95
4.2 Model Equations 96
4.3 Discretization of Derivatives with Finite Differences 98
4.4 Finite-Difference Methods for Parabolic Equations 100
4.4.1 Explicit Methods 100
4.4.2 Implicit Methods: Crank-Nicolson 105
4.4.3 An Implicit Method: Keller's Box Method 109
4.5 Finite-Difference Methods for Elliptic Equations 113
4.5.1 Direct Methods 115
4.5.2 Iterative Methods 121
4.5.3 Multigrid Method 127
References 132
Problems 132

5. Numerical Methods for Model Hyperbolic Equations 141
5.1 Introduction 141
5.2 Explicit Methods: Two-Step Lax-Wendroff Method 146
5.3 Explicit Methods: MacCormack Method 148
5.4 Implicit Methods 149
5.5 Upwind Methods 152
5.6 Finite-Volume Methods 157
5.7 Convergence and Stability 165
5.8 Numerical Dissipation and Dispersion: Artificial Viscosity 170
References 173
Problems 174