In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
will defend his dissertation
Lagrangian-Based Simplification and Feature Estimation for Flow Visualization
Vector fields are commonly used in various engineering and scientific applications for the study of different dynamical systems. Their analysis and visualization is of paramount importance to those applications. There are two different representations of vector field (or flow) data, i.e. the Eulerian representation and the Lagrangian representation. The Eulerian representation usually stores the velocity information of the flow at the grid points (i.e. spatial samples) of certain spatial discretization, while the Lagrangian representation stores the trajectories or paths of the flow particles advected by the velocity field. Recently, Lagrangian based flow representation is getting more and more attention from the computational fluid dynamics (CFD) community, especially for particle-based flow simulation (PFS) and large-scale flow simulation. For the former case, the flow information is represented by the time-dependent locations of the individual particles, while for the latter integral curves are generated and stored during simulation instead of saving the entire velocity field to achieve storage efficiency. However, most existing analysis and visualization techniques are for Eulerian-based (or mesh-based) flow data. There exists little work on the analysis of Lagrangian-based flow data, which motivates this dissertation work.
Different from the Eulerian based flow data that provides dense flow information on spatially well-distributed and fixed samples, the flow information represented by the Lagrangian way can be either very sparse (e.g., with the integral curve representation) or with complex, time-varying spatial configuration (e.g., in the PFS case), making their analysis for feature detection challenging. In addition, directly visualizing Lagrangian-based flow data (i.e. rendering the particle trajectories or integral curves provided by the data) will easily lead to clutter and occlusion. To address this challenge, this dissertation makes three contributions.
First, to analyze PFS data, a least square fitting framework for the estimation of the flow separation behavior and a Lagrangian accumulation framework for analyzing the average (or overall) physical behaviors of flow particles are introduced. Second, to reduce the clutter and occlusion issue when visualizing the Lagrangian flow data, a new and efficient geometric-based similarity metric is introduced which is combined with a number of clustering algorithms to group similar integral curves into clusters. From each cluster, one representative curve is selected to achieve a reduced representation. To evaluate the effectiveness of the new metric when compared with existing metrics, a comprehensive evaluation is performed. In particular, this evaluation considers more than 80 different combinations of the clustering techniques and similarity metrics. Their effectiveness in generating desired clustering results and reduced representations is assessed both quantitatively and qualitatively. Finally, two separation estimate strategies are introduced to identify strong separation-like behaviors from sets of integral curves, which provides the first direct solution to locating separation regions from sparse input of integral curves without reconstructing the entire vector fields. We have applied the above three techniques to a number of 2D and 3D Lagrangian flow data to demonstrate their effectiveness.
Date: Thursday, November 14, 2019
Time: 3:30 - 5:30 PM
Place: PGH 501D
Advisor: Dr. Guoning Chen
Faculty, students, and the general public are invited.