Topological methods have become standard tools in the analysis and visualization of fluid flows. Leveraging the body of mathematical work on dynamical systems they extract essential properties of complex, large scale vector fields to yield synthetic graph representations. In the special case of flows containing periodic orbits topology extraction can be applied to the induced Poincaré map. The discrete nature of this map, however, constitutes a challenge both in terms of computational cost and visual interpretation.
In the first part of this talk I will introduce standard flow visualization techniques and emphasize the topological approach used for continuous flows. I will then review previous work on Poincaré map visualization. In the second part I will report on early results of our ongoing research aimed at the automatic extraction of magnetic structures found in Tokamak reactors. The key idea of our work is to focus the analysis on the continuum underlying the Poincaré map. I will discuss the promises and challenges of this approach and conclude by pointing out interesting avenues for future work.
Joint work with Christoph Gath, University of Kaiserslautern, Germany, and Allen Sanderson, SCI Institute, University of Utah