Progressive Reference Frame Optimization for Immediate Vortex Visualization in 3D Unsteady Flow

The detection and visualization of coherent structures in unsteady fluid flow are significantly enhanced by observing the data in a reference frame that co‐moves with them. A common approach is objective reference frame optimization, which computes a frame that minimizes the perceived unsteadiness to expose these structures. Locally adapted reference frame (LARF) optimization excels at extracting small‐scale vortices in turbulent flows. However, its computational complexity restricts the method to 2D unsteady flow data in practice. The computation time grows by orders of magnitude when extending the approach to 3D. Expensive offline computation methods can be used for 3D data analysis, but hinder the immediate interactive visualization and exploration often desired. Our method enables the immediate, interactive observer‐relative visualization of 2D and 3D unsteady flow fields. We achieve high‐quality results using progressive, LARF optimization by introducing three performance optimizations. First, we integrate the system matrices via Monte Carlo sampling, enabling low‐latency previews that progressively converge to high‐quality solutions. Second, we use instantaneous vorticity deviation (IVD) as the guidance field for adaptive spatial weighting, achieving small‐scale vortex detection equivalent to FTLE. Third, we implement a visualization‐driven optimization strategy, restricting the expensive solution space to the user's current visualization domain. We validate our approach by comparison against existing offline methods, demonstrating that our framework enables interactive observer‐relative visualization using observed LIC, while preserving the high quality of expensive locally adapted vortex coreline extraction methods.