From Noisy Particle Tracks to Velocity, Acceleration and Pressure Fields using B-splines and Penalties

Abstract

Recent advances in particle tracking methods for flow measurements ([Scha14], [Scha15]) allow reconstruction of particle distributions with high particle densities that could previously only be handled with tomographic reconstruction methods. High particle densities enable reconstructions of flow fields with high spatial resolution. The STB method for tracking particles has been proven to provide more accurate estimates of particle positions without reconstructing “ghost particles” while at the same time saving time and memory compared to tomographic reconstructions. In this work, B-spline based methods for noise reduction and reconstruction of velocity, acceleration and pressure fields based on the particle track data are described and evaluated using synthetic data. The goal of these methods is to reconstruct accurate and high resolution velocity, acceleration and pressure fields. This is achieved by using the particle data directly and exploiting known physical properties such as a freedom of divergence of velocity and the Navier-Stokes equation for incompressible and uniform-density flows.