PhD Thesis 13673
Institute of Scientific Computing
Keywords: vortex cores, feature extraction, feature-based visualization, 3D vector and scalar fields, line-type features, implementation framewok for feature definition and extraction,CFD analysis, definition of a vortex, extremum lines, valley and ridge lines
Feature-based visualization deals with automatic detection of meaningful patterns in data. Which patterns are considered important depends on the domain and user requirements. Vortices are features of particular interest in fluid flow data. Many different algorithms have been published to extract vortices from flow data. Here, we focus on those detecting the center of the vortex - the vortex core line. This thesis examines existing extraction algorithms and analyzes their underlying definitions of a vortex. It proposes an elementary operation on a pair of vector fields to be used as a building block for defining and computing global line-type features of vector or scalar fields. All currently used definitions for vortex cores can be expressed in the common language of this mathematical operator. Broader categories of line-type features are also discussed: extremum lines or loci of zero curvature in a vector field, and valley or ridge lines in a scalar field. A hierarchy of feature definitions is formed and brings a common structure to the various approaches. This context allows observing relations between different feature definitions. A general problem of first-order methods with curved feature lines is identified. We propose a new definition for vortex cores based on second- order derivatives which better captures weak and curved vortices. The common mathematical operator also allows us to implement extraction algorithms for the various features by combining a few basic modules. This approach permits interactive tests of existing or new feature definitions in a modular visualization environment. The various vortex core methods are applied to practical data sets, particularly from the field of hydraulic turbomachinery (water turbines and pumps).
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