Uncertainty Reduction of FlowFit Flow Field Estimation by Use of Virtual Particle

From experiments, data is available in the form of particle pictures from which particle tracks can be inferred by tracking techniques such as tomographic PTV or Shake-The-Box. But complete knowledge of the velocity field is sought on the basis of the scattered velocity and acceleration data. For this purpose different spatial interpolation algorithms were proposed, such asFlowFit and VIC+, which take Lagrangian particle track data (position, velocity and acceleration) as input and exploit known physical properties such as continuity and the Navier-Stokes equations for incompressible and uniform-density flows to reconstruct accurate and high resolution velocity, acceleration and pressure fields. The mentioned algorithms reach higher spatial resolutions beyond Nyquist than interpolation schemes that make use of the constraint of solenoidality only, due to the increased amount of data. We aim to develope a method in which virtual particles from previous reconstructions are advected into the following interpolation timestep with an individual weight dependend on (i) the Lagrangian correlation functions known from the track data and (ii) the local velocity gradient tensor as estimated. Usually, the time steps are about the size of the Kolmogorov time scale so the Lagrangian velocities and accelerations at two subsequent time instants are still significantly correlated. Therefore, a straightforward approach to combine the information of multiple reconstructions is to involve additional virtual particles into the reconstruction process that are advected with the estimated velocity and acceleration in order to act as information carrier between the reconstructed fields, thus enforcing consistency in time.