Chebyshev spectral method and Chebyshev noise processing procedure for vorticity calculation in PIV post-processing

Abstract

Abstract Chebyshev spectral method and Chebyshev noise processing procedure are proposed for the calculation of vorticity from PIV experimental data. The Chebyshev spectral method offers superior intrinsic accuracy of derivative calculations. To overcome its noise sensitivity, the Chebyshev noise processing procedure can be applied prior to the derivative calculation to remove the high-frequency noise in the Chebyshev transform space. We compare the Chebyshev spectral method against the least-squares approach and test their performance in the calculation of vorticity with an Oseen vortex and with PIV data of the wake of a trapezoidal mixing tab. It is found that for clean velocity data the Chebyshev spectral method is extremely accurate. However, the Chebyshev spectral method alone is found to be more sensitive to noise than the least-squares method. When the Chebyshev noise processing procedure is applied together with the Chebyshev spectral method it greatly reduces the error and makes the Chebyshev spectral method more accurate than the least-squares method for a wide range of vorticity values. A special requirement imposed by the Chebyshev spectral method is that the PIV velocity processing must be carried out on special grids such as Gauss–Lobatto points.