Divergence-free smoothing for volumetric PIV data

This paper proposes a divergence-free smoothing (DFS) method for the post-process of volumetric particle image velocimetry (PIV) data, which can smooth out noise and divergence error at the same time. The method is a combination of the penalized least squares regression and the divergence corrective scheme (DCS), employing the generalized cross-validation method to automatically determine the best smoothing parameter. By introducing a weight-changing algorithm similar to the all-in-one method, a robust version of DFS can simultaneously deal with vector validation, replacement of outliers and missing vectors, smoothing, and zero-divergence correction of the velocity field. Direct numerical simulation data of turbulent channel flow (Johns Hopkins Turbulence Databases) added with artificial noise, outliers and missing vectors are used to test the accuracy of DFS. The results show that DFS can smooth the velocity field to divergence-free and performs better than the all-in-one method, DCS and some other available conventional processing methods for post-process of velocity field, especially in dealing with clustered outliers and missing vectors. A block DFS is suggested to process large velocity field to save both time and memory. Tests on tomographic PIV data validate the effectiveness of DFS on improving both flow statistics and flow visualization.