Steadification of Unsteady Vector Fields for Flow Visualization

• Applicant: Professor Dr.-Ing. Holger Theisel
• Subject Area: Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing ; Software Engineering and Programming Languages
• Term: from 2016 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 309227598

• Final Report Year: 2022

Final Report Abstract

We have developed approaches to represent an unsteady flow field v(x,t) by a new vector field w(x,t) such that the path lines of v correspond to the stream lines of w. This was motivated by the following observation: Stream lines in steady (as well as unsteady) vector fields are much better explored and understood than path lines. There are some reasons for this: • Historically, Flow visualization was concerned with steady vector fields first before moving to unsteady ones. For steady flows, stream lines are the relevant lines to be considered. • Stream lines are invariant under scaling of the (steady or unsteady) vector field, while scaling of an unsteady field will generally change the path lines. • Stream lines do not have self-intersections, path lines generally do. • Stream lines can usually be integrated until infinity (unless the boundary of the spatial domain is reached), whereas path lines can usually be integrated only over a finite time interval. Beside these advantages, stream lines have big drawback: they have no physical meaning in unsteady flow fields (contrary to path lines that describe the trajectories of unsteady particles. We formulated the problem as an optimization problem where both the unknown field w and the location of cuts in w are searched simultaneously. The result is a steady visualization of unsteady flow fields where the flow dynamics are encoded in the steady representation. In addition, we developed a modified version of the well-known double gyre test data set that has - contrary to the original formulation - a closed-form solution of the hyperbolic trajectory. We applied this ground truth data set to evaluate existing approaches for the extraction of Lagrangian Coherent Structures in timedependent vector fields.

Publications

• A Modified Double Gyre with Ground Truth Hyperbolic Trajectories for Flow Visualization. Computer Graphics Forum, 2020
  S. Wolligandt, T. Wilde, C. Rössl and H Theisel
  
• Lagrangian Q-criterion and Transport of Salt and Temperature. IEEE Scientific Visualization Contest, 2020
  S. Wolligandt, J. Zimmermann, T. Wilde, M. Motejat and H. Theisel
  
• Static Visualization of Unsteady Flows by Flow Steadification. Proc. of Vision, Modeling, and Visualization, 2020
  S. Wolligandt, T. Wilde, C. Rössl and H. Theisel