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.
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 two techniques for accelerating their computation, based on
adaptive mesh refinement and on grid advection.