Page 8 - Basic Structured Grid Generation

Contents vii

5.13.2 Subdirectory: Book/one.d.gds 150
5.13.3 Subdirectory: Book/hyper.gds 150
5.13.4 Subdirectory: Book/p.d.Equations 151

6. Variational methods and adaptive grid generation 152
6.1 Introduction 152
6.2 Euler-Lagrange equations 153
6.3 One-dimensional grid generation 157
6.3.1 Variational approach 157
6.3.2 Dynamic adaptation 159
6.3.3 Space-curves 161
6.4 Two-dimensional grids 164
6.4.1 The L-functional and the Winslow model 165
6.4.2 The weighted L-functional 166
6.4.3 The weighted area-functional 167
6.4.4 Orthogonality-functional 167
6.4.5 Combination of functionals 168
6.4.6 Other orthogonality functionals 169
6.4.7 The Liao functionals 170
6.4.8 Surface grids 171
6.5 Harmonic maps 172
6.5.1 Surface grids 175
6.6 Website programs 177
6.6.1 Subdirectory: Book/var.gds 177
6.6.2 Subdirectory: Book/one.d.gds 179

7. Moving grids and time-dependent co-ordinate systems 180
7.1 Time-dependent co-ordinate transformations 180
7.2 Time-dependent base vectors 181
7.3 Transformation of generic convective terms 184
7.4 Transformation of continuity and momentum equations 185
7.4.1 Continuity equation 185
7.4.2 Momentum equations 185
7.5 Application to a moving boundary problem 187
8. Unstructured grid generation 190
8.1 Introduction 190
8.2 Delaunay triangulation 191
8.2.1 Basic geometric properties 191
8.2.2 The Bowyer-Watson algorithm 193
8.2.3 Point insertion strategies 196
8.3 Advancing front technique (AFT) 203
8.3.1 Introduction 203
8.3.2 Grid control 204
8.3.3 Searching algorithm 205
8.3.4 AFT algorithm 206