A Meshless And Binless Approach To Compute Statistics In 3D Ensemble PTV

Abstract

We propose a method to obtain super-resolution of turbulent statistics for three-dimensional ensemble particle tracking velocimetry (EPTV). Our approach is “meshless” because it does not require a grid to compute derivatives, and it is “binless” because it does not require bins to compute local statistics. The method combines the constrained radial basis function (RBF) formalism introduced in Sperotto et al. (Meas Sci Technol, 33:094005, 2022) with a kernel estimate approach for the ensemble average of the RBF regressions. The computational cost for the RBF regression is alleviated with the partition of unity method (PUM). We compare the newly proposed method with traditional binning-based approaches such as Gaussian weighting (Agüí and Jiménez, JFM, 185:447-468, 1987) and local polynomial fitting (Agüera et al, Meas Sci Technol, 27:124011, 2016). The results on experimental data of an underwater jet show a better resolution of spatial gradients of turbulent stresses while at the same time yielding an analytical expression which results in super-resolution of statistical quantities.