  Accurately and efficiently measuring the pressure field is of paramount
importance in many fluid mechanics applications. The pressure gradient field of
a fluid flow can be determined from the balance of the momentum equation based
on the particle image velocimetry (PIV) measurement of the flow kinematics,
which renders the experimental evaluation of the material acceleration and the
viscous stress terms possible. We present a novel method of reconstructing the
pressure fields from error-embedded pressure gradient measurement data. This
method utilized Green's function of the Laplacian operator as the convolution
kernel that relates pressure to pressure gradient. A compatibility condition on
the boundary offers equations to solve for the boundary pressure. This Green's
function integral (GFI) method has a deep mathematical connection with the
state-of-the-art omnidirectional integration (ODI). As mathematically
equivalent to ODI in the limit of an infinite number of line integral paths,
GFI spares the necessity of line integration along zigzag integral paths,
rendering generalized implementation schemes for both two and three-dimensional
problems with arbitrary geometry while bringing in improved computational
efficiency. In the current work, we apply GFI to pressure reconstruction of
simple canonical and isotropic turbulence flows embedded with error in
two-dimensional and three-dimensional domains, respectively. Uncertainty
quantification is performed by eigenanalysis of the GFI operator in a square
domain. The accuracy and computational efficiency of GFI are evaluated and
compared with ODI.
