The accuracy of remapping irregularly spaced velocity data onto a regular grid and the computation of vorticity

Abstract

The velocity data obtained from molecular tagging velocimetry (MTV) are typically located on an irregularly spaced measurement grid. To take advantage of many standard data processing techniques, the MTV data need to be remapped onto a grid with a uniform spacing. In this work, accuracy and noise issues related to the use of a least-squares-fit to various low order polynomials for the remapping of these data onto a uniformly spaced grid and the subsequent computation of vorticity from these data are examined. This information has relevance to PIV data processing as well. It has been previously noted that the best estimate of the velocity vector acquired through the use of tracer techniques such as PIV, is at the midpoint of the displacement vector. Thus, unless special care is taken, PIV data are also initially obtained on an irregular grid. The error in the remapped velocity and the calculated vorticity field is divided into a mean bias error and a random error. In the majority of cases, the mean bias error is a more significant source of error than the more often quoted random error. Results of the simulation show that the best choice for remapping is the use of a least-squares fit to a 2nd order polynomial and the best choice for vorticity calculation is to use a 4th order accurate, central, finite difference applied to uniformly sampled data. The actual value of the error depends upon the data density and the radius used for the selection of velocity measurements to be included in the remapping process. Increasing the data density and reducing the fit radius improve the accuracy.