Extracting Flow Structures Using Sparse Particles

In recent years, Lagrangian Coherent Structures (LCS) have been characterized using the Finite-Time Lyapunov Exponent, following the advection of a dense set of particles into a corresponding flow field. The large amount of particles needed to sufficiently map a flow field has been a non-trivial computational burden in the application of LCS. By seeding a minimal amount of particles into the flow field, Moving Least Squares, combined with FTLE, will extrapolate the important feature locations at which further refinement is desired. Following the refinement procedure, MLS produces a continuous function reconstruction allowing the characterization of Lagrangian Coherent Structures with a lower number of particles. Through multiple data sets, we show that given a sparse and refined sampling, MLS will reproduce FTLE fields exhibiting a nominal error while maintaining a performance increase when compared to the standard, dense finite difference approach.