Uses and Misuses of Topology in Numerical Flow Visualization

Numerical flow visualization is gaining importance because of the continuing trend from experiments toward computational fluid dynamics. We have come to the situation where reliable numerical data are easily available but often hard to interpret because their size and intricacy challenge current visualization tools. The state of the art in flow visualization is advancing on several fronts, an important one being the field of feature-based visualization, which aims at revealing flow features such as vortices, flow separation, or recirculation. Such flow phenomena are of interest because of their effect, either beneficial or adverse, in industrial applications like power generation, mixing, or combustion. Feature-based flow visualization again splits into several branches, but one of them has become particularly popular under the name of vector field topology.

In this talk we present work in topology-based flow visualization, resulting from our collaboration with turbomachinery companies and focusing on the optimization of water turbines. We discuss the usage of vector field topology for extracting the above mentioned flow features, and additional ones such as vortex rings and vortex breakdown bubbles. We address the limitations of vector field topology and the current search for an adequate extension to unsteady flow fields. Finally we move to the field of Lagrangian coherent structures, which can be interpreted as a time-dependent variant of vector field topology. There, we present a technique for accelerating their computation, based on adaptive mesh refinement.