Performance analysis and application of grid interpolation techniques for fluid flows

Abstract

Although it is common for automated image processing techniques to claim subpixel accuracy in the identification of particles, or centroids of displacements of groups of particles, additional errors are inevitably introduced when and if these data are reinterpolated back onto a grid mesh whose nodes lie at different locations from the original data. Moreover, these errors can be large compared to the errors introduced in the original image processing step.

Two different techniques, convolution with an adaptive Gaussian window (AGW), and a two-dimensional thin-shell spline (STS), have been compared and contrasted for interpolating irregularly spaced data onto a regular grid. Both techniques are global interpolators; the Gaussian kernel applies an ad hoc choice of smooth function, while the thin-shell spline minimises a global functional proportional to the Laplacian of the velocity field. In this way, the smoothness constraint on the spline coefficients may be thought of as akin to a viscous smoothing of the fluid flow.

Performance curves are given, enabling the investigator to make an informed choice of interpolating routine and grid interpolation parameters to minimise the interpolation errors, given various external constraints. Some illustrative example applications on real experimental data are described. In general, the importance of matching the interpolation technique to the characteristics of the original data is stressed. It is also pointed out that a correct interpretation of grid interpolated data must be based on a basic knowledge of the performance characteristics of that interpolator. Finally, recommendations are made concerning the development of surface spline techniques for problems involving large numbers of data points.