Optimal Transport for Particle Image Velocimetry: Real Data and Postprocessing Algorithms

Particle image velocimetry (PIV) is a method used to measure the velocity field of a fluid flow. Traditionally, cross correlation algorithms are used to retrieve the flow velocity. Recently, a new method for PIV based on the L optimal mass transportation problem (OT-PIV), is introduced and analyzed in [Saumier, Khouider and Agueh, Optimal Transport for Particle Image Velocimetry, Comm. Math. Sci., Vol. 13, No. 1, 269–296, 2015] for the case of synthetically generated data and for particles of equal mass or brightness. Here, we extend the work of Saumier et al. (2015) to the case of particles with different masses and randomly seeded particles. More importantly, we compare the OT-PIV method with a typical cross-correlation algorithm for the case of real data. Using a combination of theory and numerical experiments, we demonstrate that in the presence of particles with different weights/brightness, the OT method is more accurate for the largest/brightest particles, and it is more faithful when the particles are far enough from each other. This makes it more suitable for the so-called particle tracking regime of PIV, i.e, when the seeding density is low. We demonstrate in particular that for low seeding densities, the OT method performs better than a typical cross-correlation algorithm. Based on these new results and the previous ones in Saumier et al. (2015), we propose a suite of post-processing algorithms for the OT-PIV method. It is found that the OT-PIV with post-processing performs very well on the synthetic and real data when compared to the cross-correlation method.