Grid-free planar method of Particle Image Velocimetry

Today, the method of PIV (Particle Image Velocimetry) is widely used in the field of experimental fluid mechanics due to its high reliability in solving practical problems. However, it has a known limitation associated with errors that occur when calculating velocity derivatives, which are necessary to deform the processed PIV images while improving the performance of the method. Since the number of errors increases with the use of higher order schemes, in practice it is most often limited to the first order, which in turn leads to a decrease in spatial resolution. In the present research, we propose a method that allows the schemes of more than the second order, which significantly improves the accuracy of measuring velocity and its derivatives, and thereby increases the spatial resolution. The method does not require the recovery of erroneous velocity vectors, avoids the numerical calculation of velocity derivatives, and is easily applied in practice.