Chapter 4 Vortex detection - Computer Graphics and Visualization

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Colour Plates Colour Plate 7: Pipe flow with particle paths and a slice coloured with pressure. (See also Fig. 6.16a on p. 113.) Colour Plate 8: Pipe flow with semi-transparent isosurfaces approximating vortices and selective streamlines through the regions. (See also Fig. 6.21 on p. 117.) 141
Summary This thesis describes the extraction and visualization of geometries in fluid flows, with the goal of gaining insight into important features of the flow. Geometries are curves, surfaces, and volumes, which have the advantage that they can be easily perceived by the human visual system, and efficiently rendered by computers. Chapter 2 contains a survey of related work in the field of geometric techniques. This serves as a framework for placing the techniques covered in the following chapters into context. Chapter 3 covers ‘particle tracing’, a technique which simulates massless particles transported by a flow. By calculating and visualizing the particle paths, information is obtained about the flow features. Complications are caused by the use of grids with irregularly formed cells, or with irregular topologies. In such grids, point location (determining which cell contains a certain particle) is a problem. This chapter describes particle tracing techniques for curvilinear grids, for so-called -transformed grids, and for unstructured grids. In curvilinear grids consisting of hexahedral cells, the problem can be solved by decomposing the cells into 5 tetrahedra. In -transformed grids, where the cells are often strongly deformed, this method is inadequate. This can be solved by decomposing the cells into 6 tetrahedra. In unstructured grids, the cells are often tetrahedra, but extra connectivity information must be added to solve the point location problem. Once this information has been derived, particle tracing in unstructured grids is well possible. Chapter 4 covers techniques for detecting vortices, an important class of flow features. These techniques may employ two types of criteria: physical criteria and geometric criteria. The first category is based on physical quantities, such as pressure and vorticity. It has turned out that these criteria do not detect all vortices; especially weak vortices, characterized by low velocities, are often missed. The second category, which uses geometric criteria, is only based upon shape properties of flow curves, such as particle paths. It is assumed that vortices are characterized by rotational movement, which leads to circular particle paths. In this category, two methods have been developed and evaluated: one method is based on the curvature centres of curves, another on their winding-angles. It turns out that the curvature centre method is quite sensitive to not perfectly circular vortices, in which case it does not detect them. The winding-angle method often does find weak and non-circular vortices. In addition, 143
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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 p 1 α
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Chapter 4. Vortex detection (a) (c)
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Chapter 5 Deformable surfaces ÁÒ
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Surface Creation Surface Deformatio
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normvelo a= velo/len(velo) velograd
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5.3.1 Node displacement 5.3. Surfac
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5.3. Surface deformation of the ran
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C λ l λ 3 λ 2 λ 1 λ r λ 5.4.
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5.4. Surface refinement high cost f
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5.5. Examples Figure 5.11: Miller
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Page 134 and 135: Bibliography EKATERINIS, J.A., & SC
Page 136 and 137: Bibliography MILLER, J.V. 1990. On
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