Models for Particle Image Velocimetry: Optimal Transportation and Navier-Stokes Equations

• Main Author: Saumier Demers, Louis-Philippe
• Other Authors: Agueh, Martial
• Language: English; en
• Published: 2016
• Subjects: Optimal Transport; Navier-Stokes Equations; Particle Image Velocimetry; Numerical Algorithm; Mathematical Model; Image Processing
• Online Access: http://hdl.handle.net/1828/7041

We introduce new methods based on the L2 Optimal Transport (OT) problem and the Navier-Stokes equations to approximate a fluid velocity field from images obtained with Particle Image Velocimetry (PIV) measurements. The main idea is to consider two successive images as the initial and final densities in the OT problem, and to use the associated OT flow as an estimate of the underlying physical flow. We build a simple but realistic model for PIV data, and use it to analyze the behavior of the transport map in this situation. We then design and implement a series of post-processing filters created to improve the quality of the numerical results, and we establish comparisons with traditional cross-correlation algorithms. These results indicate that the OT-PIV procedure performs well on low to medium seeding densities, and that it gives better results than typical cross-correlation algorithms in some cases. Finally, we use a variational method to project the OT velocity field on the space of solutions of the Navier-Stokes equations, and extend it to the rest of the fluid domain, outside the particle locations. This extension provides an effective filtering of the OT solution beyond the local post-processing filters, as demonstrated by several numerical experiments. === Graduate