On the role of domain-specific knowledge in the visualization of technical flows

In this paper, we present an overview of a number of existing flow visualization methods, developed by the authors in the recent past, that are specifically aimed at integrating and leveraging domain-specific knowledge into the visualization process. These methods transcend the traditional divide between interactive exploration and featurebased schemes and allow a visualization user to benefit from the abstraction properties of feature extraction and topological methods while retaining intuitive and interactive control over the visual analysis process, as we demonstrate on a number of examples

Visualization of intricate flow structures for vortex breakdown analysis

Journal ArticleVortex breakdowns and flow recirculation are essential phenomena in aeronautics where they appear as a limiting factor in the design of modern aircrafts. Because of the inherent intricacy of these features, standard flow visualization techniques typically yield cluttered depictions. The paper addresses the challenges raised by the visual exploration and validation of two CFD simulations involving vortex breakdown. To permit accurate and insightful visualization we propose a new approach that unfolds the geometry of the breakdown region by letting a plane travel through the structure along a curve. We track the continuous evolution of the associated projected vector field using the theoretical framework of parametric topology. To improve the understanding of the spatial relationship between the resulting curves and lines we use direct volume rendering and multi-dimensional transfer functions for the display of flow-derived scalar quantities. This enriches the visualization and provides an intuitive context for the extracted topological information. Our results offer clear, synthetic depictions that permit new insight into the structural properties of vortex breakdowns

Eyelet particle tracing - steady visualization of unsteady flow

It is a challenging task to visualize the behavior of time-dependent 3D vector fields. Most of the time an overview of unsteady fields is provided via animations, but, unfortunately, animations provide only transient impressions of momentary flow. In this paper we present two approaches to visualize time varying fields with fixed geometry. Path lines and streak lines represent such a steady visualization of unsteady vector fields, but because of occlusion and visual clutter it is useless to draw them all over the spatial domain. A selection is needed. We show how bundles of streak lines and path lines, running at different times through one point in space, like through an eyelet, yield an insightful visualization of flow structure ('eyelet lines'). To provide a more intuitive and appealing visualization we also explain how to construct a surface from these lines. As second approach, we use a simple measurement of local changes of a field over time to determine regions with strong changes. We visualize these regions with isosurfaces to give an overview of the activity in the dataset. Finally we use the regions as a guide for placing eyelets

Localized Flow and Analysis of 2D and 3D Vector Fields

In this paper we present an approach to the analysis of the contribution of a small subregion in a dataset to the global flow. To this purpose, we subtract the potential flow that is induced by the boundary of the sub-domain from the original flow. Since the potential flow is free of both divergence and rotation, the localized flow field retains the original features. In contrast to similar approaches, by making explicit use of the boundary flow of the subregion, we manage to isolate the region-specific flow that contains exactly the local contribution of the considered subdomain to the global flow. In the remainder of the paper, we describe an implementation on unstructured grids in both two and three dimensions. We discuss the application of several widely used feature extraction methods on the localized flow, with an emphasis on topological schemes

Automatic Image Based Time Varying 3D Feature Extraction and Tracking

3D time-varying data sets are complex. The intrinsics of those data cannot be readily comprehended by users solely based on visual investigation. Computational tools such as feature extraction and tracking are often necessary. Until now, most existing algorithms in this domain work effectively in the object space, relying on prior knowledge of the data. How to find a more flexible and efficient method which can perform automatically to implement extraction and tracking remains an attractive topic. This thesis presents a new image-based method that extracts and tracks the 3D time- varying volume data sets. The innovation of the proposed approach is two-fold. First, all analyses are performed in the image space on volume rendered images without accessing the actual volume data itself. The image-based processing will help to both save storage space in the memory and reduce computation burden. Secondly, the new approach does not require any prior knowledge of the user-defined “feature” or a built model. All the parameters used by the algorithms are automatically determined by the system itself, thus flexibility and efficiency can be achieved at the same time. The proposed image-based feature extraction and tracking system consists of four components: feature segmentation (or extraction), feature description (or shape analysis), classification, and feature tracking. Feature segmentation is to identify and label individual features from the image so that we can describe and track them separately. We combine both region-based and edge-based segmentation approaches to implement the extraction process. Feature description is to analyze each feature and derive a vector to describe the feature such that the subsequent tracking step does not have to rely on the entire feature extracted, but instead a much smaller and informative feature descriptor. Classification is to identify the corresponding features from two consecutive image frames along both the time and the spatial domain. Feature tracking is to study and model the evolution of features based on the correspondence computation result from classification stage. Experimental results show that the image-based feature extraction and tracking system provides high fidelity with great efficiency

Computation of Localized Flow for Steady and Unsteady Vector Fields and its Applications

We present, extend, and apply a method to extract the contribution of a subregion of a data set to the global flow. To isolate this contribution, we decompose the flow in the subregion into a potential flow that is induced by the original flow on the boundary and a localized flow. The localized flow is obtained by subtracting the potential flow from the original flow. Since the potential flow is free of both divergence and rotation, the localized flow retains the original features and captures the region-specific flow that contains the local contribution of the considered subdomain to the global flow. In the remainder of the paper, we describe an implementation on unstructured grids in both two and three dimensions for steady and unsteady flow fields. We discuss the application of some widely used feature extraction methods on the localized flow and describe applications like reverse-flow detection using the potential flow. Finally, we show that our algorithm is robust and scalable by applying it to various flow data sets and giving performance figures

Visual Analysis of Spatia-temporal Relations of Pairwise Attributes in Unsteady Flow

Despite significant advances in the analysis and visualization of unsteady flow, the interpretation of it’s behavior still remains a challenge.In this work, we focus on the linear correlation and non-linear dependency of different physical attributes of unsteady flows to aid theirstudy from a new perspective. Specifically, we extend the existing spatial correlation quantification, i.e. the Local Correlation Coefficient(LCC), to the spatio-temporal domain to study the correlation of attribute-pairs from both the Eulerian and Lagrangian views. To studythe dependency among attributes, which need not be linear, we extend and compute the mutual information (MI) among attributes overtime. To help visualize and interpret the derived correlation and dependency among attributes associated with a particle, we encodethe correlation and dependency values on individual pathlines. Finally, to utilize the correlation and MI computation results to identifyregions with interesting flow behavior, we propose a segmentation strategy of the flow domain based on the ranking of the strengthof the attributes relations. We have applied our correlation and dependency metrics to a number of 2D and 3D unsteady flows withvarying spatio-temporal kernel sizes to demonstrate and assess their effectiveness

Spectral, Combinatorial, and Probabilistic Methods in Analyzing and Visualizing Vector Fields and Their Associated Flows

In this thesis, we introduce several tools, each coming from a different branch of mathematics, for analyzing real vector fields and their associated flows. Beginning with a discussion about generalized vector field decompositions, that mainly have been derived from the classical Helmholtz-Hodge-decomposition, we decompose a field into a kernel and a rest respectively to an arbitrary vector-valued linear differential operator that allows us to construct decompositions of either toroidal flows or flows obeying differential equations of second (or even fractional) order and a rest. The algorithm is based on the fast Fourier transform and guarantees a rapid processing and an implementation that can be directly derived from the spectral simplifications concerning differentiation used in mathematics. Moreover, we present two combinatorial methods to process 3D steady vector fields, which both use graph algorithms to extract features from the underlying vector field. Combinatorial approaches are known to be less sensitive to noise than extracting individual trajectories. Both of the methods are extensions of an existing 2D technique to 3D fields. We observed that the first technique can generate overly coarse results and therefore we present a second method that works using the same concepts but produces more detailed results. Finally, we discuss several possibilities for categorizing the invariant sets with respect to the flow. Existing methods for analyzing separation of streamlines are often restricted to a finite time or a local area. In the frame of this work, we introduce a new method that complements them by allowing an infinite-time-evaluation of steady planar vector fields. Our algorithm unifies combinatorial and probabilistic methods and introduces the concept of separation in time-discrete Markov chains. We compute particle distributions instead of the streamlines of single particles. We encode the flow into a map and then into a transition matrix for each time direction. Finally, we compare the results of our grid-independent algorithm to the popular Finite-Time-Lyapunov-Exponents and discuss the discrepancies. Gauss\'' theorem, which relates the flow through a surface to the vector field inside the surface, is an important tool in flow visualization. We are exploiting the fact that the theorem can be further refined on polygonal cells and construct a process that encodes the particle movement through the boundary facets of these cells using transition matrices. By pure power iteration of transition matrices, various topological features, such as separation and invariant sets, can be extracted without having to rely on the classical techniques, e.g., interpolation, differentiation and numerical streamline integration

Critical points in two-dimensional stationary homogeneous isotropic turbulence

Basic properties of critical points in two dimensions are reviewed and related to the velocity and acceleration field of two-dimensional turbulence. A direct numerical simulation (DNS) of two-dimensional homogeneous isotropic turbulence with an inverse energy cascade and a k−5/3 power law is used to study critical points of these fields. The velocity stagnation point based pair separation model of Goto and Vassilicos (S Goto and J C Vassilicos, 2004, New J.Phys., 6, p.65) is revisited and placed on a sound mathematical foundation. The DNS is used to study the time-asymmetry observed between forward and backward separation. A new method has been employed to obtain values for the Richardson constants and the ratio of them for the backwards and forwards case, which is gb/gf = (0.92±0.03) and hence, exhibits a qualitatively different behaviour from pair separation in three-dimensional turbulence, where gb > gf (J Berg et al. , 2006, Phys.Rev.E, 74(1), p.016304). An explanation for this behaviour based on the timeasymmetry related to the inverse versus forward energy cascade is suggested. Zero Acceleration Points (ZAPs) and flow structures around them are studied using the same DNS. A well-defined classification of ZAPs in terms of the acceleration gradient tensor’s (∇a) invariants is presented. About half of all ZAPs are Anti-ZAPs (with det[∇a] 0) is about the same. Vortical and straining ZAPs are swept by the local fluid velocity to a good statistical approximation whereas Anti-ZAPs are not. The average life-time of ZAPs seems to scale with the time-scale of the smallest eddies in the turbulence, though ZAPs (in particular vortical ones) are able to survive up to a few integral time scales. The new ZAP classification can also be applied to extended flow regions and a discussion of the length-scales and sizes characterising these regions and the distances between ZAPs is given