A Particle-Based Approach to Extract Dynamic 3D FTLE Ridge Geometry

Lagrangian coherent structures (LCS) is an important concept for the visualization of unsteady flows. They describe the boundaries of regions for which material transport stays mostly coherent over time which can help for a better understanding of dynamical systems. One of the most common techniques for their computation is the extraction of ridges from the finite-time Lyapunov exponent (FTLE) field. FTLE ridges are challenging to extract, both in terms of accuracy and performance, because they expose strong gradients of the underlying field, tend to come close to each other and are dynamic with respect to different time parameters. We present a new method for extracting FTLE ridges for series of integration times which is able to show how coherent regions and their borders evolve over time. Our techniques mainly build on a particle system which is used for sampling the ridges uniformly. This system is highly optimized for the challenges of FTLE ridge extraction. Further, it is able to take advantage of the continuous evolvement of the ridges which makes their sampling for multiple integration times much faster. We test our method on multiple 3D datasets and compare it to the standard Marching Ridges technique. For the extraction examples our method is 13 to over 300 times faster, suggesting a significant advantage. We efficiently extract Lagrangian coherent structures (LCS) as ridges of the finite-time Lyapunov Exponent (FTLE) for series of integration times. Our methods build on a particle system which is highly optimized for the challenges of the FTLE ridge extraction and takes advantage of the continuous evolvement of ridges over time. image