Post-processing of volumetric PIV data based on continuity condition

A new technique of data post-processing was proposed to improve volumetric velocity field of particle image velocimetry (PIV). To make the processed velocity field satisfy the differential form of the continuity equation of incompressible flow, the modification was made on the original experimental data. The correcting velocity field was obtained by solving the minimum problem of its 2-norm using the method of Lagrange multipliers. Mathematical proof was provided to demonstrate that the modified velocity field was a better approximation of the true flow. Simulation of an analytical flow with noise was performed to further prove that the post-processing technique can reduce the common Gaussian noise of PIV measurements. The technique is successfully applied to a volumetric PIV data, which indicates that it can improve the smoothness of the velocity field as well.