Topology tracking for the visualization of time-dependent two-dimensional flows

Abstract

The paper presents a topology-based visualization method for time-dependent two-dimensional vector elds. A time interpolation enables the accurate tracking of critical points and closed orbits as well as the detection and identication of structural changes. This completely characterizes the topology of the unsteady ow. Bifurcation theory provides the theoretical framework. The results are conveyed by surfaces that separate subvolumes of uniform ow behavior in a three-dimensional space-time domain.

Topological Methods for Visualizing Vortical Flows

“…Complete 3D topology has not been attempted yet, however there are authors that examine subsets, such as Globus et al [6] and Theisel et al [17] using saddle connectors. Tricoche et al [18] describe how the time-tracking of singularities and the corresponding topological variations can be investigated for instationary 2D vector fields. Theisel and Seidel also propose a method for the tracking of critical points in more general settings by integrating streamlines of the derived feature flow field [16].…”

“…The method was originally designed for time-dependent 2D vector fields [18] and has been recently extended to the 3D case [5]. We focus the description hereafter on the latter case, which is in essence very similar to the planar case.…”

“…This is not a drawback of our algorithm but rather a limitation inherent in this class of tracking algorithms (cf. [18,16]) If this information is assumed given, the running times for our examples are on the order of very few seconds. Since the algorithm only needs two successive time steps to do its work, it is possible to integrate it directly into the CFD simulation.…”

“…As mentioned previously we can now abstract these data from their original embedding in three-space and treat them as the successive states of a parameter-dependent planar vector field. In that way we can apply the two-dimensional tracking scheme proposed in [18] and whose extension to three dimensions was discussed in the previous section. In essence the setting of the original method corresponds here to the computational space.…”

Eyelet Particle Tracing - Steady Visualization of Unsteady Flow

“…While Reinders et al use their graph view to ease the navigation through single time steps and to show events like birth, death and annihilation of features over time, Garth et al show the movement of singularities relative to a given axis. Concerning time-dependent vector field topology the most advanced approaches we found in literature were proposed by Tricoche et al [19] and Theisel et al [17]. Unfortunately both are only dealing with 2D time-varying fields.…”