Toward an improved method for the interpolation and differentiation of particle tracking velocimetry data

Abstract

An approach is presented in two and three dimensions for the employment of natural-neighbor techniques to improve the efficiency of interpolating scattered PTV data. Velocity and vorticity were interpolated for an artificial Lamb-Oseen vortex in two dimensions and an artificial Burgers vortex in three dimensions. Gradient calculations were performed using finite differences on the generated interpolants in two and three dimensions; additionally, the natural-neighbor shape functions were differentiated to compute gradients directly in two dimensions. Natural-neighbor interpolation was found to offer a significant savings in both setup and computational time when compared to RBF interpolation. Both methods offered low average relative error across the domains, with the relative accuracy between methods dependent on the problem. Neither technique was found to significantly amplify or filter noise in the data. Further investigation is necessary to refine the use of natural-neighbor methods for PTV, but such algorithms offer a promising direction for accurate rapid interpolation and differentiation of sparse and dense flow information.