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

Chebyshev spectral method and Chebyshev noise processing procedure are prop osed for the calculation of vorticity from PIV experimental data. The Cheby shev spectral method offers superior intrinsic accuracy of derivative calcu lations. 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 Cheby shev spectral method against the least-squares approach and test their perf ormance in the calculation of vorticity with an Oseen vortex and with PIV d ata of the wake of a trapezoidal mixing tab. It is found that for clean vel ocity data the Chebyshev spectral method is extremely accurate. However, th e Chebyshev spectral method alone is found to be more sensitive to noise th an the least-squares method. When the Chebyshev noise processing procedure is applied together with the Chebyshev spectral method it greatly reduces t he error and makes the Chebyshev spectral method more accurate than the lea st-squares method for a wide range of vorticity values. A special requireme nt imposed by the Chebyshev spectral method is that the PIV velocity proces sing must be carried out on special grids such as Gauss-Lobatto points. (C) 2001 Elsevier Science Inc. All rights reserved.