Green's function integral method for pressure reconstruction from measured pressure gradient and the interpretation of omnidirectional integration

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