Inferring volumetric data from PTV measurements of incompressible flows

A novel method is proposed to spatially reconstruct a divergence-free velocity from Particle Tracking Velocimetry (PTV) measurements of incompressible flow. Current methods for a general flow first interpolate the scattered PTV data onto a fixed Eulerian grid using a predetermined number of particles around each grid point. This limits the achievable accuracy as the particles move along their Lagrangian trajectories and the density of the particles around each fixed grid point changes in time. Our method avoids a fixed Eulerian grid and directly uses the Lagrangian PTV data to reconstruct velocities with maximum accuracy. At each instant, a very high-degree rational polynomial is fitted to the scattered PTV velocities and then projected to be divergence-free on a dynamic triangulation that encompasses the particles. Arnoldi-based methods are presented for numerically reliable computation of the high-degree fit and projection. The proposed method is shown to outperform the widely used radial basis functions in both accuracy and speed for certain functions. The method is applied on data ranging from simulated flows to experimental PTV measurements.