Contents
1 Introduction 1
1.1 Background . . . . 1
1.2 Scope and methodology of the thesis . . . . 2
1.3 Thesis outline . . . . 5
2 Hierarchical grid generation approach 7 2.1 Model definition . . . . 7
2.2 Hierarchical parameters specification for hybrid grid generation . . . . 10
2.2.1 Hybrid generation flags . . . 11
2.2.2 Anisotropic parameters . . . 12
2.2.3 Isotropic parameters . . . 14
2.2.4 Source entities . . . 15
2.3 Hierarchical grid generation . . . 16
3 Unstructured simplicial grid generation 19 3.1 Introduction . . . 19
3.2 Delaunay triangulation . . . 22
3.2.1 Definition and properties . . . 22
3.2.2 Construction methods . . . 24
3.2.2.1 The Bowyer-Watson algorithm . . . 24
3.2.2.2 Bowyer-Watson primitive operations . . . 25
3.2.2.3 Robustness and round-off error . . . 26
3.2.2.4 Performance . . . 27
3.3 Isotropic simplicial grid generation . . . 27
3.3.1 General unstructured grid generation scheme . . . 27
3.3.2 Boundary recovery . . . 31
3.3.3 Background grid . . . 35
3.3.4 Internal point generation . . . 37
3.3.5 Grid optimization . . . 42
3.3.5.1 Element quality . . . 45
3.3.5.2 Smoothing . . . 46
3.3.5.3 Local modifications . . . 47
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3.3.5.4 Optimization strategy . . . 48
3.3.5.5 Performance . . . 48
3.4 Anisotropic simplicial grid generation . . . 49
3.4.1 Metrics and distances . . . 51
3.4.2 Metric definition . . . 53
3.4.3 Anisotropic Delaunay triangulation . . . 54
3.4.4 Anisotropic internal point creation . . . 56
3.4.5 Anisotropic optimization . . . 57
4 Hybrid surface grid generation 59 4.1 Introduction . . . 59
4.2 Hybrid edge grid generation . . . 62
4.2.1 Edge parametric representation . . . 62
4.2.2 Semi-structured edge grid generation . . . 63
4.2.3 Unstructured edge grid generation . . . 64
4.3 Hybrid face grid generation . . . 66
4.3.1 Face parametric representation . . . 66
4.3.2 Semi-structured face grid generation . . . 68
4.3.2.1 Hyperbolic grid generation equations . . . 70
4.3.2.2 Discretization and boundary conditions . . . 70
4.3.2.3 Modifications for surface hyperbolic grid generation . 71 4.3.2.4 Termination criteria . . . 72
4.3.2.5 Example . . . 73
4.3.3 Unstructured face grid generation . . . 73
4.3.3.1 The two-dimensional Delaunay triangulation . . . 74
4.3.3.2 Surface internal point creation . . . 74
4.3.3.3 Example . . . 75
4.4 Automatic isotropic parameter specification . . . 76
4.4.1 Introduction . . . 76
4.4.2 Automatic curvature-based edge grid generation . . . 78
4.4.3 Automatic curvature-based face grid generation . . . 80
5 Semi-structured volume grid generation 83 5.1 Introduction . . . 83
5.2 Semi-structured hexahedral/prismatic grid generation . . . 87
5.2.1 General scheme . . . 87
5.2.2 Computation of marching directions . . . 90
5.2.3 Computation of marching distances . . . 93
5.2.4 Termination criteria . . . 94
5.2.5 Interfacing with the unstructured grid generator . . . 95
5.3 Generalized fronts . . . 97 5.3.1 One-dimensional generalized fronts for surface grid generation 97
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5.3.2 Two-dimensional generalized fronts for volume grid generation 99
5.4 Front unfolding . . . 101
5.5 Front folding . . . 104
6 Results 109 6.1 Surface grid examples . . . 109
6.2 Unstructured grid examples . . . 114
6.3 Hybrid grid examples . . . 119
6.4 Validation . . . 122
7 Conclusions and perspectives 127 7.1 Conclusions . . . 127
7.2 Perspectives . . . 128
Bibliography 131
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