Page 11 - Introduction to Computational Fluid Dynamics

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CONTENTS
6.2.6 Overall Calculation Procedure May 27, 2005 0:54
171
6.2.7 Node Tagging and Boundary Conditions 172
6.3 Unstructured Meshes 174
6.3.1 Main Task 174
6.3.2 Gauss’s Divergence Theorem 177
6.3.3 Construction of a Line Structure 179
6.3.4 Convective Transport 180
6.3.5 Diffusion Transport 181
6.3.6 Interim Discretised Equation 182
6.3.7 Interpolation of at P 2 ,E 2 , a, and b 183
6.3.8 Final Discretised Equation 184
6.3.9 Evaluation of Nodal Gradients 186
6.3.10 Boundary Conditions 186
6.3.11 Pressure-Correction Equation 190
6.3.12 Method of Solution 192
6.3.13 Overall Calculation Procedure 193
6.4 Applications 194
6.5 Closure 207
Exercises 209

7. Phase Change.....................................214
7.1 Introduction 214
7.2 1D Problems for Pure Substances 216
7.2.1 Exact Solution 216
7.2.2 Simple Numerical Solution 217
7.2.3 Numerical Solution Using TDMA 221
7.2.4 Accurate Solutions on a Coarse Grid 222
7.3 1D Problems for Impure Substances 225
Exercises 230

8. Numerical Grid Generation ....................... 233

8.1 Introduction 233
8.2 Algebraic Grid Generation 233
8.2.1 1D Domains 233
8.2.2 2D Domains 234
8.3 Differential Grid Generation 235
8.3.1 1D Domains 235
8.3.2 2D Domains 237
8.3.3 Inversion of Determinant Equations 238
8.4 Sorenson’s Method 241
8.4.1 Main Specifications 241
8.4.2 Stretching Functions 243