A meshless and binless approach to compute statistics in 3D ensemble PTV

We propose a method to obtain super-resolution of turbulent statistics for three-dimensional ensemble particle tracking velocimetry (EPTV). The method is “meshless” because it does not require the definition of a grid for computing derivatives, and it is “binless” because it does not require the definition of bins to compute local statistics. The method combines the constrained radial basis function (RBF) formalism introduced Sperotto et al. (Meas Sci Technol 33:094005, 2022) with an ensemble trick for the RBF regression of flow statistics. The computational cost for the RBF regression is alleviated using the partition of unity method (PUM). Three test cases are considered: (1) a 1D illustrative problem on a Gaussian process, (2) a 3D synthetic test case reproducing a 3D jet-like flow, and (3) an experimental dataset collected for an underwater jet flow at \(\text {Re} = 6750\) $\text{Re}=6750$ using a four-camera 3D PTV system. For each test case, the method performances are compared to traditional binning approaches such as Gaussian weighting (Agüí and Jiménez in JFM 185:447–468, 1987), local polynomial fitting (Agüera et al. in Meas Sci Technol 27:124011, 2016), as well as binned versions of RBFs.