Topological methods for visualizing vortical flows

Abstract

The paper describes the application of topological methods to the visualization of vortical flow patterns that arise in simulations from Computational Fluid Dynamics. Two techniques are presented: the first is concerned with the exploration of complicated, instantaneous flow structures while the second one permits the visualization of their temporal evolution in large-scale transient simulations. In both cases the mathematical framework is derived from the notion of parametric topology. This yields a unified formalism that permits to efficiently address the challenges raised by typical flow problems. The benefits of this approach are demonstrated in the analysis and visualization of transient vortical flows that undergo the phenomenon of vortex breakdown.