Chapter 4 Vortex detection - Computer Graphics and Visualization

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Figure 6.21: Selective streamlines and isosurfaces of Q Figure 6.22: Selective streamlines and ellipoid icons 6.3. A transitional pipe ßow 117
Chapter 6. Applications 6.4 The Delta-Wing aircraft The data set used here is the Delta-Wing data set made available by NASA Ames Research Center. It models the ßow around a Delta-Wing aircraft at a 40 degrees angle of attack [Ekaterinis & Schiff, 1990]. The features in this data set include vortices on one side of the wing. The original Þles contain the following quantities: density, momentum, and stagnation, which are deÞned on a ¢ ¢ structured curvilinear grid. In this application, we use particle tracing, vortex detection techniques, and deformable surfaces. 6.4.1 Particle tracing (a) Projected to the xz-plane (b) Best view on vortex Figure 6.23: Delta-Wing with particle traces The Þgures show that the vortices are not parallel with any of the natural axes, or even to any of the and -planes in computational space. This makes it difÞcult to apply one of the 2D vortex detection techniques. Therefore, we apply a 3D approach for vortex extraction, namely deformable surfaces (see Chapter 5). 6.4.2 Vortex detection using deformable surfaces As in Section 6.3.1, the visualization with particle tracing has shown that the vortices in this data set are not aligned with one of the natural coordinate axes. In this case, we may apply deformable surfaces (see Chapter 5, as they have the advantage that they are inherently 3D, rather than limited to 2D projections. To detect vortices, the deformable surface technique can be applied with two types of deformation criteria: scalar criteria and vector criteria. 118
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Extraction and Visualization of Geo
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Extraction and Visualization of Geo
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Preface The research described in t
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Contents 1 Introduction 1 1.1 Scien
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Contents 6.2.4 Vortex detection wit
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Chapter 1. Introduction Figure 1.1:
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Chapter 2 Geometry extraction techn
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2.1. Fields and grids their geometr
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2.3. Surfaces ¯ hyperstreamline: a
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2.3. Surfaces in a local coordinate
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2.4. Deformable models from some in
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2.4. Deformable models where ÜÖ
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2.5. Vortices There are several imp
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2.5. Vortices contours called Simpl
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Chapter 3. Particle Tracing initial
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Chapter 3. Particle Tracing a decre
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Chapter 3. Particle Tracing 3.3 Par
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Chapter 3. Particle Tracing Figure
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Chapter 3. Particle Tracing (a) h =
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Chapter 3. Particle Tracing F B E H
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Chapter 3. Particle Tracing nodes w
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Chapter 3. Particle Tracing 3.5 Exa
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Chapter 3. Particle Tracing (a) fra
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Chapter 3. Particle Tracing 4.249 4
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Chapter 3. Particle Tracing 42 (a)
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Chapter 3. Particle Tracing 44 Figu
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Chapter 3. Particle Tracing Figure
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Chapter 4. Vortex detection 4.1 Phy
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Chapter 4. Vortex detection Figure
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Chapter 4. Vortex detection (a) (b)
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Chapter 4. Vortex detection indicat
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Chapter 4. Vortex detection 4.3.2 E
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Chapter 4. Vortex detection 58 Figu
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Chapter 4. Vortex detection Figure
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Chapter 4. Vortex detection Û. Unf
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Chapter 4. Vortex detection y 6 4 2
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Page 78 and 79: Chapter 5 Deformable surfaces ÁÒ
Page 80 and 81: Surface Creation Surface Deformatio
Page 82 and 83: normvelo a= velo/len(velo) velograd
Page 84 and 85: 5.3.1 Node displacement 5.3. Surfac
Page 86 and 87: 5.3. Surface deformation of the ran
Page 88 and 89: C λ l λ 3 λ 2 λ 1 λ r λ 5.4.
Page 90 and 91: 5.4. Surface refinement high cost f
Page 92 and 93: 5.5. Examples Figure 5.11: Miller
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Page 96 and 97: velorot a= rot(velo) velohd a= dot(
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Page 100 and 101: Chapter 6 Applications This chapter
Page 102 and 103: Figure 6.1: PaciÞc Ocean; streamli
Page 104 and 105: y 80 70 60 50 40 30 20 10 0 0 20 40
Page 106 and 107: y 80 70 60 50 40 30 20 10 0 0 20 40
Page 108 and 109: (a) Top view of a horizontal grid s
Page 110 and 111: (a) Frame 0 (b) Frame 40 6.2. The B
Page 112 and 113: (a) Vorticity magnitude (b) Normali
Page 114 and 115: y 6130 6120 6110 6100 6090 6080 607
Page 116 and 117: Number of clusters 15 Number of CW
Page 118 and 119: (a) (b) 6.3. A transitional pipe ß
Page 120 and 121: (a) Ô (b) (c) (d) É 6.3. A tran
Page 122 and 123: Figure 6.19: isosurface of high É
Page 126 and 127: Deformable surfaces with scalar cri
Page 128 and 129: 6.4. The Delta-Wing aircraft (a) In
Page 130 and 131: Chapter 7. Conclusions and future w
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Page 134 and 135: Bibliography EKATERINIS, J.A., & SC
Page 136 and 137: Bibliography MILLER, J.V. 1990. On
Page 138 and 139: Bibliography SADARJOEN, I.A., VAN W
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Page 142 and 143: Colour Plates Colour Plate 3: Backw
Page 144 and 145: Colour Plates Colour Plate 7: Pipe
Page 146 and 147: Summary this method offers the capa
Page 148 and 149: Samenvatting methode gebaseerd op k
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