Page 10 - Introduction to Computational Fluid Dynamics

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CONTENTS
4.9 Overall Procedure 91 May 27, 2005 0:54 ix
4.9.1 Calculation Sequence 91
4.9.2 Initial Conditions 92
4.9.3 Choice of Step Size and Iterations 93
4.10 Applications 93
Exercises 101
5. 2D Convection– Cartesian Grids ................ . 105

5.1 Introduction 105
5.1.1 Main Task 105
5.1.2 Solution Strategy 106
5.2 SIMPLE – Collocated Grids 109
5.2.1 Main Idea 109
5.2.2 Discretisation 110
5.2.3 Pressure-Correction Equation 112
5.2.4 Further Simplification 117
5.2.5 Overall Calculation Procedure 119
5.3 Method of Solution 120
5.3.1 Iterative Solvers 120
5.3.2 Evaluation of Residuals 121
5.3.3 Underrelaxation 122
5.3.4 Boundary Conditions for 123
5.3.5 Boundary Condition for p 125
m
5.3.6 Node Tagging 126
5.4 Treatment of Turbulent Flows 128
5.4.1 LRE Model 128
5.4.2 HRE Model 129
5.5 Notion of Smoothing Pressure Correction 133
5.6 Applications 139
Exercises 152

6. 2D Convection– Complex Domains ............. . 161
6.1 Introduction 161
6.1.1 Curvilinear Grids 161
6.1.2 Unstructured Grids 162
6.2 Curvilinear Grids 164
6.2.1 Coordinate Transformation 164
6.2.2 Transport Equation 165
6.2.3 Interpretation of Terms 166
6.2.4 Discretisation 168
6.2.5 Pressure-Correction Equation 170