Topology-Based Methods in Visualization II (eBook)

Preface 5
Contents 7
Visualization of Coherent Structures in Transient 2D Flows 9
1 Introduction 9
2 The Finite-Time Lyapunov Exponent 10
3 Previous Work 11
4 Visualization of Coherent Structures 12
5 Results 15
6 Discussion 19
References 21
Visualizing Lagrangian Coherent Structures and Comparison to Vector Field Topology 22
1 Introduction 22
2 Lagrangian Coherent Structures 23
3 Results 26
4 Conclusion 35
References 35
Extraction of Separation Manifolds using Topological Structures in Flow Cross Sections 37
1 Introduction 37
2 Related Work 39
3 Extracting Separation Manifolds 40
4 Results 44
5 Conclusion 47
References 48
Topology Based Selection and Curation of Level Sets 50
1 Introduction 50
2 Preliminary 55
3 Algorithm 57
4 Results 60
5 Conclusion 61
References 61
Representing Interpolant Topology for Contour Tree Computation 64
1 Introduction 64
2 The Contour Tree 65
3 Join and Split Graphs 68
4 Graph Widgets for Standard Interpolants 68
5 Finite State Machines for Split Graphs 70
6 Marching (Hyper)Cubes and Digital Images 73
7 Implementation and Results 75
8 Conclusions and Future Work 76
References 77
Path Line Attributes - an Information Visualization Approach to Analyzing the Dynamic Behavior of 3D Time- Dependent Flow Fields 79
1 Introduction 79
2 Related Work 81
3 Path Line Attributes 81
4 System overview 83
5 Applications 85
6 Conclusions 90
References 91
Flow Structure based 3D Streamline Placement 93
1 Introduction 93
2 Related Work 94
3 Construction of Flow Structures 95
4 Flow Structure Examples 95
5 Streamline Seeding 97
6 Sparse Seeding 99
7 Results 100
8 Conclusion 103
References 103
Critical Points of the Electric Field from a Collection of Point Charges 105
1 Introduction 105
2 Electric Potential and Field 106
3 Octree Method for Finding Critical Points 106
4 Finding a Sphere Containing all the Critical Points 108
5 Results 114
References 118
Visualizing global manifolds during the transition to chaos in the Lorenz system 119
1 Introduction 119
2 Global manifolds as a collection of geodesic level sets 120
3 Visualizing the Lorenz manifold 123
4 Transition through the homoclinic explosion 125
5 Intersections of two-dimensional manifolds 127
6 Conclusions 128
References 129
Streamline and Vortex Line Analysis of the Vortex Breakdown in a Confined Cylinder Flow 131
1 Introduction 131
2 Numerical Experiment of the Lid Driven Cylinder Flow 134
3 Phenomenological Description Of Vortex Breakdown 135
4 Topological Analysis 137
5 Local Flow Analysis 140
6 Conclusion 145
References 146
Flow Topology Beyond Skeletons: Visualization of Features in Recirculating Flow 149
1 Introduction 149
2 Topology of vortex rings 151
3 Analytical vortex ring model 153
4 Visualization techniques for vortex rings 155
5 Results 158
6 Conclusion 162
References 162
Bringing Topology-Based Flow Visualization to the Application Domain 165
1 Introduction 165
2 Application: Simulation of In-Cylinder Flow 167
3 Application: Heat Transfer 168
4 Application: Spinning Missile 170
5 Application Independent Directions 175
6 Summary and Conclusions 176
References 177
Computing Center-Lines: An Application of Vector Field Topology 181
1 Introduction 181
2 Related Work 182
3 Methodology 183
4 Results 187
5 Conclusions and Future Work 191
References 192