Flow in Frames - Optimal Sets of Reference Frames 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
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 563742222

The visual analysis of flows strongly depends on the coordinate system (reference frame) in which the flow is observed. Observation in different moving reference frames reveals different features. This raised the demand for features and properties that only depend on the flow and not on the particular reference system. To get such objective visualizations (i.e., representations that do not depend on a chosen moving frame), a common approach is reference frame optimization by steadification. Reference frame optimization is a hard problem that strongly depends on the chosen flow domain. If the domain is too small, the problem is under-defined. If the domain is too large, the problem is over-defined, allowing only approximate solutions. Up to now, only trivial shapes of flow domains have been considered: local neighbourhoods, or the whole global flow domain. In the project, we propose to combine reference frame optimization with flow domain optimization. In particular, we simultaneously search for optimal frames in optimal flow domains. Further, we search for a small number of optimal frames representing the entire flow, resulting in frame clustering approaches. We also propose nested reference frames to cover vortical behavior at different scales. Finally, we propose to restrict the search for optimal frames to those in which the Navier-Stokes equations can be observed.

• DFG Programme: Research Grants