High-resolution particle-based 3D velocimetry using divergence-free radial basis functions

We present a new method of inferring high-resolution 3D divergence-free velocity fields from particle image tomograms. This method – termed tomographic particle flow velocimetry (T-PFV) – is based on representing the velocity field as a linear combination of divergence-free radial basis functions; the piece-wise constant representation of the estimated velocity field that is inherent to tomographic particle image velocimetry (T-PIV) is replaced by a smooth representation that automatically satisfies conservation of mass. The appropriate linear combination is determined using a non-regularized optical flow framework. We provide a detailed evaluation of T-PFV in terms of accuracy, spatial resolution, and sensitivity to parameters based on 3D constant-density DNS data. We also show that T-PFV yields substantial improvements in accuracy and spatial resolution compared to T-PIV over a wide range of parameters.