Vector Field Topology of Time-Dependent Flows in a Steady Reference Frame

Baeza Rojo I, Günther T (2020)

Publication Type: Journal article

Publication year: 2020

Journal

IEEE Transactions on Visualization and Computer Graphics Institute of Electrical and Electronics Engineers (IEEE)

Book Volume: 26

Pages Range: 280-290

Article Number: 8805446

Journal Issue: 1

DOI: 10.1109/TVCG.2019.2934375

Abstract

The topological analysis of unsteady vector fields remains to this day one of the largest challenges in flow visualization. We build up on recent work on vortex extraction to define a time-dependent vector field topology for 2D and 3D flows. In our work, we split the vector field into two components: A vector field in which the flow becomes steady, and the remaining ambient flow that describes the motion of topological elements (such as sinks, sources and saddles) and feature curves (vortex corelines and bifurcation lines). To this end, we expand on recent local optimization approaches by modeling spatially-varying deformations through displacement transformations from continuum mechanics. We compare and discuss the relationships with existing local and integration-based topology extraction methods, showing for instance that separatrices seeded from saddles in the optimal frame align with the integration-based streakline vector field topology. In contrast to the streakline-based approach, our method gives a complete picture of the topology for every time slice, including the steps near the temporal domain boundaries. With our work it now becomes possible to extract topological information even when only few time slices are available. We demonstrate the method in several analytical and numerically-simulated flows and discuss practical aspects, limitations and opportunities for future work.

Authors with CRIS profile

Tobias Günther

Involved external institutions

Eidgenössische Technische Hochschule Zürich (ETHZ) / Swiss Federal Institute of Technology in Zurich

Switzerland (CH)

How to cite

APA:

Baeza Rojo, I., & Günther, T. (2020). Vector Field Topology of Time-Dependent Flows in a Steady Reference Frame. IEEE Transactions on Visualization and Computer Graphics, 26(1), 280-290. https://dx.doi.org/10.1109/TVCG.2019.2934375

MLA:

Baeza Rojo, Irene, and Tobias Günther. "Vector Field Topology of Time-Dependent Flows in a Steady Reference Frame." IEEE Transactions on Visualization and Computer Graphics 26.1 (2020): 280-290.

BibTeX: Download