Analysis and Visualization of Vortices: Topological, Physics-Based and Deep Learning Techniques
Berenjkoub, Marzieh 1986-
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Vector fields, especially flow, and their analysis are of paramount importance to a wide variety of scientific and engineering applications. Despite significant advances in the analysis and visualization of vector fields, the interpretation of their behavior still remains a challenge. There are different flow features that are of interest to different applications. Among them, vortices are the main subject for the study of turbulence flows. Vortices characterize the rotational behavior of the flow and they are responsible for the transportation of materials and energy. Despite their importance, there currently does not exist an effective way to identify and characterize vortices due to the lack of a unified definition of vortices. To address that, this research proposes three different approaches to analyze and visualize vortices based on their geometric and physical characteristics. The first approach characterizes the circulating pattern of vortices using a topology-based analysis, while the second approach identifies vortices based on their unique physics. The third approach uses a deep learning method to identify the boundaries of vortices, a traditionally difficult and unsolved problem. This dissertation provides detailed description and discussion on each of these three approaches. The proposed methods and their visualization have been applied to a number of 2D and 3D steady and unsteady flows to evaluate their effectiveness. Important flow characteristics that cannot be revealed with the previous methods are captured by the proposed methods.