Benchmarking Data Assimilation Algorithms For 3D Lagrangian Particle Tracking

Abstract

This paper reports a comparison of three state-of-the-art data assimilation (DA) algorithms for 3D Lagrangian particle tracking (LPT): Vortex-In-Cell sharp (VIC#), FlowFit3, and neural-implicit particle advection (NIPA). Particle trajectories, termed “tracks,” are spatially sparse, and a reconstruction algorithm is commonly employed to estimate dense Eulerian fields using position, velocity, and/or acceleration data from the tracks. DA algorithms for LPT combine the tracks with a set of governing equations (or constraints) to enhance the accuracy of the velocity field, relative to interpolation methods, and infer additional quantities like pressure. We compare the performance of VIC#, FlowFit3, and NIPA with respect to their accuracy and computational cost. Accuracy is assessed in terms of the mean inter-particle distance, frame rate, and magnitude of tracking errors, and costs are reported in wall time. Synthetic and experimental data sets for homogeneous isotropic turbulence and turbulent boundary layer flows are evaluated; direct numerical simulations are used for the synthetic tests, and realistic localization errors are added to the simulated tracks. All three DA methods perform well in cases with the highest spatio-temporal sampling of the flow, and all three methods are relatively robust to the frame rate and magnitude of localization errors. NIPA is more resilient to sparse seeding than FlowFit or VIC#, which exhibit similar performance, but NIPA is also the most expensive technique by some margin. DA reconstructions are superior to interpolation across the board, with a reduction of error up to 80% in the experimental demonstration.