A recursive interpolation algorithm for particle tracking velocimetry

A new type of interpolation algorithm for particle tracking velocimetry is proposed. The algorithm is established based on a combination of ellipsoidal differential equations, i.e. a recursive process from a lower to a higher order interpolation. Each equation is solved as a boundary value problem by using the discrete velocity vector information as boundary conditions. In this paper the performance of the interpolation scheme, such as errors and cross correlations, is examined using the Taylor–Green vortex flow and isotropic turbulent flow. The examination results reveal that the recursive process from linear to hexagonal interpolation provides the best reconstruction in comparison to the single process. A quantitative evaluation is also carried out for integral and derivative information of the velocity vector, such as stream function and vorticity.