Vector fields are a common concept for the representation of many different kinds of flow phenomena in science and engineering. Topology-based methods have shown their convenience for visualizing and analyzing steady flow but a counterpart for unsteady flow is still missing. However, a lot of good and relevant work has been done aiming at such a solution. We give an overview of the research done on the way towards topology-based visualization of unsteady flow, pointing out the different approaches and methodologies involved as well as their relation to each other, taking classical (i.e. steady) vector field topology as our starting point. Particularly, we focus on Lagrangian Methods, Space-Time Domain Approaches, Local Methods, and Stochastic and Multi-Field Approaches. Furthermore, we illustrated our review with practical examples for the different approaches.

The analysis of time-dependent data is often guided by the question of how dominant structures develop over time. It is important to understand how patterns or structures identified for one time step evolve over time, by changing or moving in the domain. To gain insight into such evolving structural change it is crucial to effectively compare different time steps. This paper proposes a comparison method for twodimensional flow fields. The method is based on a feature description using invariant moments. The specific strength of these moments is their invariance under scaling and rotation, thus facilitating an identification of features even if they occur at other positions, with changed orientation, and variation in size. In addition the moments themselves can be used to define a similarity measure. To evaluate the significance of this concept it has been applied to wind speed data from meteorological simulations. 1

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Abstract A key approach to visualizing a flow field is to emphasize regions with significant behavior. However, it is difficult to give concrete criteria for classifying feature regions. In this paper, we use a novel framework in which fuzzy sets are used to determine flow features: Fuzzy relationships assess structural properties of features. A fuzzy c-means-like clustering algorithm is used to evaluate the importance of each voxel. Our approach can be readily modified with new fuzzy relationships describing other features of interest to users. We use a multi-resolution approach which displays structural features in greater detail, and represents the background by coarse-grained information. Experiments on synthetic and real datasets show that our framework can highlight significant aspects of the whole flow while avoiding occlusion and clutter. Interactive performance is achieved via a GPU implementation.

Abstract—Understanding the hemodynamics of blood flow in vascular pathologies such as aneurysms is essential for both their diagnosis and treatment. Computational fluid dynamics (CFD) simulations of blood flow based on patient-individual data are performed to better understand aneurysm initiation and progression and for predicting treatment success. A CFD simulation results in a complex, multiparameter dataset comprising scalar as well as vectorial data attributes. For its comprehensive investigation, the contained flow information is often visualized by a highly dense and cluttered set of integral curves colored according to one of the attributes. We aim at a fully automatic approach for reducing visual clutter and exposing characteristic flow structures by grouping similar curves and computing group representatives. In this work, we lay the foundations by evaluating different clustering techniques for grouping curves. We evaluate Spectral Clustering and four versions of Agglomerative Hierarchical Clustering. Both are particularly suited since they can be based on inter-curve distances rendering the construction of feature vectors unnecessary. Our work focuses on steadystate