Spectral decomposition-based fast pressure integration algorithm

Reconstructing pressure fields from 2D or 3D velocimetry data involves a pressure gradient integration procedure. This paper proposes a spectral decomposition-based fast pressure integration (SD-FPI) algorithm to integrate a gridded pressure gradient field. The algorithm seeks the least-square solution for the discrete momentum conservation equation by matrix decompositions, which allows for the use of various difference schemes. The recently proposed fast Fourier transform (FFT) integration method (Huhn et al. Exp Fluids 57:151, 2016) could be viewed as a special example of SD-FPI when adopting a special circulant difference scheme. The inherent relationship between SD-FPI and the Poisson reconstruction is also revealed in theory. An iterative strategy for SD-FPI is developed to integrate the pressure gradient fields with missing data. The accuracy and efficiency of SD-FPI with various difference schemes including the FFT-based approaches are compared based on a synthetic pressure field. We conclude that while the computing efficiency is always high, the accuracy of SD-FPI depends on the difference scheme and error types of the pressure gradients.