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Accurately and efficiently measuring the pressure field is of paramountimportance in many fluid mechanics applications. The pressure gradient field ofa fluid flow can be determined from the balance of the momentum equation basedon the particle image velocimetry (PIV) measurement of the flow kinematics,which renders the experimental evaluation of the material acceleration and theviscous stress terms possible. We present a novel method of reconstructing thepressure fields from error-embedded pressure gradient measurement data. Thismethod utilized Green's function of the Laplacian operator as the convolutionkernel that relates pressure to pressure gradient. A compatibility condition onthe boundary offers equations to solve for the boundary pressure. This Green'sfunction integral (GFI) method has a deep mathematical connection with thestate-of-the-art omnidirectional integration (ODI). As mathematicallyequivalent 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-dimensionalproblems with arbitrary geometry while bringing in improved computationalefficiency. In the current work, we apply GFI to pressure reconstruction ofsimple canonical and isotropic turbulence flows embedded with error intwo-dimensional and three-dimensional domains, respectively. Uncertaintyquantification is performed by eigenanalysis of the GFI operator in a squaredomain. The accuracy and computational efficiency of GFI are evaluated andcompared with ODI.

Green's Function Integral method for Pressure Reconstruction from Measured Pressure Gradient and the Interpretation of Omnidirectional Integration