Doctor of Philosophy

dissertationWith modern computational resources rapidly advancing towards exascale, large-scale simulations useful for understanding natural and man-made phenomena are becoming in- creasingly accessible. As a result, the size and complexity of data representing such phenom- ena are also increasing, making the role of data analysis to propel science even more integral. This dissertation presents research on addressing some of the contemporary challenges in the analysis of vector fields--an important type of scientific data useful for representing a multitude of physical phenomena, such as wind flow and ocean currents. In particular, new theories and computational frameworks to enable consistent feature extraction from vector fields are presented. One of the most fundamental challenges in the analysis of vector fields is that their features are defined with respect to reference frames. Unfortunately, there is no single ""correct"" reference frame for analysis, and an unsuitable frame may cause features of interest to remain undetected, thus creating serious physical consequences. This work develops new reference frames that enable extraction of localized features that other techniques and frames fail to detect. As a result, these reference frames objectify the notion of ""correctness"" of features for certain goals by revealing the phenomena of importance from the underlying data. An important consequence of using these local frames is that the analysis of unsteady (time-varying) vector fields can be reduced to the analysis of sequences of steady (time- independent) vector fields, which can be performed using simpler and scalable techniques that allow better data management by accessing the data on a per-time-step basis. Nevertheless, the state-of-the-art analysis of steady vector fields is not robust, as most techniques are numerical in nature. The residing numerical errors can violate consistency with the underlying theory by breaching important fundamental laws, which may lead to serious physical consequences. This dissertation considers consistency as the most fundamental characteristic of computational analysis that must always be preserved, and presents a new discrete theory that uses combinatorial representations and algorithms to provide consistency guarantees during vector field analysis along with the uncertainty visualization of unavoidable discretization errors. Together, the two main contributions of this dissertation address two important concerns regarding feature extraction from scientific data: correctness and precision. The work presented here also opens new avenues for further research by exploring more-general reference frames and more-sophisticated domain discretizations

ANALYSIS AND VISUALIZATION OF FLOW FIELDS USING INFORMATION-THEORETIC TECHNIQUES AND GRAPH-BASED REPRESENTATIONS

Three-dimensional flow visualization plays an essential role in many areas of science and engineering, such as aero- and hydro-dynamical systems which dominate various physical and natural phenomena. For popular methods such as the streamline visualization to be effective, they should capture the underlying flow features while facilitating user observation and understanding of the flow field in a clear manner. My research mainly focuses on the analysis and visualization of flow fields using various techniques, e.g. information-theoretic techniques and graph-based representations. Since the streamline visualization is a popular technique in flow field visualization, how to select good streamlines to capture flow patterns and how to pick good viewpoints to observe flow fields become critical. We treat streamline selection and viewpoint selection as symmetric problems and solve them simultaneously using the dual information channel [81]. To the best of my knowledge, this is the first attempt in flow visualization to combine these two selection problems in a unified approach. This work selects streamline in a view-independent manner and the selected streamlines will not change for all viewpoints. My another work [56] uses an information-theoretic approach to evaluate the importance of each streamline under various sample viewpoints and presents a solution for view-dependent streamline selection that guarantees coherent streamline update when the view changes gradually. When projecting 3D streamlines to 2D images for viewing, occlusion and clutter become inevitable. To address this challenge, we design FlowGraph [57, 58], a novel compound graph representation that organizes field line clusters and spatiotemporal regions hierarchically for occlusion-free and controllable visual exploration. We enable observation and exploration of the relationships among field line clusters, spatiotemporal regions and their interconnection in the transformed space. Most viewpoint selection methods only consider the external viewpoints outside of the flow field. This will not convey a clear observation when the flow field is clutter on the boundary side. Therefore, we propose a new way to explore flow fields by selecting several internal viewpoints around the flow features inside of the flow field and then generating a B-Spline curve path traversing these viewpoints to provide users with closeup views of the flow field for detailed observation of hidden or occluded internal flow features [54]. This work is also extended to deal with unsteady flow fields. Besides flow field visualization, some other topics relevant to visualization also attract my attention. In iGraph [31], we leverage a distributed system along with a tiled display wall to provide users with high-resolution visual analytics of big image and text collections in real time. Developing pedagogical visualization tools forms my other research focus. Since most cryptography algorithms use sophisticated mathematics, it is difficult for beginners to understand both what the algorithm does and how the algorithm does that. Therefore, we develop a set of visualization tools to provide users with an intuitive way to learn and understand these algorithms

Surface-based flow visualization

This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier and can be found at: http://www.journals.elsevier.com/computers-and-graphics/.With increasing computing power, it is possible to process more complex fluid simulations. However, a gap between increasing\ud data size and our ability to visualize them still remains. Despite the great amount of progress that has been made in the field of\ud flow visualization over the last two decades, a number of challenges remain. Whilst the visualization of 2D flow has many good\ud solutions, the visualization of 3D flow still poses many problems. Challenges such as domain coverage, speed of computation, and\ud perception remain key directions for further research. Flow visualization with a focus on surface-based techniques forms the basis\ud of this literature survey, including surface construction techniques and visualization methods applied to surfaces. We detail our\ud investigation into these algorithms with discussions of their applicability and their relative strengths and drawbacks. We review the\ud most important challenges when considering such visualizations. The result is an up-to-date overview of the current state-of-the-art\ud that highlights both solved and unsolved problems in this rapidly evolving branch of research

Visitation Graphs: Interactive Ensemble Visualization with Visitation Maps

Modern applications in computational science are increasingly focusing on understanding uncertainty in models and parameters in simulations. In this paper, we describe visitation graphs, a novel approximation technique for the well-established visualization of steady 2D vector field ensembles using visitation maps. Our method allows the efficient and robust computation of arbitrary visitation maps for vector field ensembles. A pre-processing step that can be parallelized to a high degree eschews the needs to store every ensemble member and to re-calculate every time the start position of the visitation map is changed. Tradeoffs between accuracy of generated visitation maps on one side and pre-processing time and storage requirements on the other side can be made. Instead of downsampling ensemble members to a storable size, coarse visitation graphs can be stored, giving more accurate visitation maps while still reducing the amount of data. Thus accurate visitation map creation is possible for ensembles where the traditional visitation map creation is prohibitive. We describe our approach in detail and demonstrate its effectiveness and utility on examples from Computational Fluid Dynamics

Fundamentals and Applications of N-pulse Particle Image Velocimetry-accelerometry: Towards Advanced Measurements of Complex Flows and Turbulence

abstract: Over the past three decades, particle image velocimetry (PIV) has been continuously growing to become an informative and robust experimental tool for fluid mechanics research. Compared to the early stage of PIV development, the dynamic range of PIV has been improved by about an order of magnitude (Adrian, 2005; Westerweel et al., 2013). Further improvement requires a breakthrough innovation, which constitutes the main motivation of this dissertation. N-pulse particle image velocimetry-accelerometry (N-pulse PIVA, where N>=3) is a promising technique to this regard. It employs bursts of N pulses to gain advantages in both spatial and temporal resolution. The performance improvement by N-pulse PIVA is studied using particle tracking (i.e. N-pulse PTVA), and it is shown that an enhancement of at least another order of magnitude is achievable. Furthermore, the capability of N-pulse PIVA to measure unsteady acceleration and force is demonstrated in the context of an oscillating cylinder interacting with surrounding fluid. The cylinder motion, the fluid velocity and acceleration, and the fluid force exerted on the cylinder are successfully measured. On the other hand, a key issue of multi-camera registration for the implementation of N-pulse PIVA is addressed with an accuracy of 0.001 pixel. Subsequently, two applications of N-pulse PTVA to complex flows and turbulence are presented. A novel 8-pulse PTVA analysis was developed and validated to accurately resolve particle unsteady drag in post-shock flows. It is found that the particle drag is substantially elevated from the standard drag due to flow unsteadiness, and a new drag correlation incorporating particle Reynolds number and unsteadiness is desired upon removal of the uncertainty arising from non-uniform particle size. Next, the estimation of turbulence statistics utilizes the ensemble average of 4-pulse PTV data within a small domain of an optimally determined size. The estimation of mean velocity, mean velocity gradient and isotropic dissipation rate are presented and discussed by means of synthetic turbulence, as well as a tomographic measurement of turbulent boundary layer. The results indicate the superior capability of the N-pulse PTV based method to extract high-spatial-resolution high-accuracy turbulence statistics.Dissertation/ThesisAnimation of N-pulse PIVA measurement of flow-structure interactionDoctoral Dissertation Mechanical Engineering 201

Visuelle Analyse großer Partikeldaten

Partikelsimulationen sind eine bewährte und weit verbreitete numerische Methode in der Forschung und Technik. Beispielsweise werden Partikelsimulationen zur Erforschung der Kraftstoffzerstäubung in Flugzeugturbinen eingesetzt. Auch die Entstehung des Universums wird durch die Simulation von dunkler Materiepartikeln untersucht. Die hierbei produzierten Datenmengen sind immens. So enthalten aktuelle Simulationen Billionen von Partikeln, die sich über die Zeit bewegen und miteinander interagieren. Die Visualisierung bietet ein großes Potenzial zur Exploration, Validation und Analyse wissenschaftlicher Datensätze sowie der zugrundeliegenden Modelle. Allerdings liegt der Fokus meist auf strukturierten Daten mit einer regulären Topologie. Im Gegensatz hierzu bewegen sich Partikel frei durch Raum und Zeit. Diese Betrachtungsweise ist aus der Physik als das lagrange Bezugssystem bekannt. Zwar können Partikel aus dem lagrangen in ein reguläres eulersches Bezugssystem, wie beispielsweise in ein uniformes Gitter, konvertiert werden. Dies ist bei einer großen Menge an Partikeln jedoch mit einem erheblichen Aufwand verbunden. Darüber hinaus führt diese Konversion meist zu einem Verlust der Präzision bei gleichzeitig erhöhtem Speicherverbrauch. Im Rahmen dieser Dissertation werde ich neue Visualisierungstechniken erforschen, welche speziell auf der lagrangen Sichtweise basieren. Diese ermöglichen eine effiziente und effektive visuelle Analyse großer Partikeldaten