Abstract
Based on the least squares and Radial Basis Function (RBF), we propose to use a robust method to reconstruct the velocity gradient and strain/rotation-rate tensor from Lagrangian Particle Tracking (LPT) data. A stable RBF method, RBF-QR, is employed to provide robust approximation in the flat limit of shape functions without suffering ill-conditioning. Least squares method enables the reconstruction of noisy data and further improves the robustness of the calculation on realistic experimental data. The use of Partition-of-Unity Method (PUM) localizes the calculation and allows handling large data set in 2D and 3D and improves computational efficiency. The accuracy and robustness of the method is validated on both 2D and 3D simulated LPT data with artificial noise based on Direct Numerical Simulation (DNS). The technique is further tested on the 3D LPT data obtained from a synthetic jet experiment.
