Pressure Field Reconstruction from Particle Image Velocimetry Data Using Analytical Solutions of the Pressure Poisson Equation for a set of Problems with Mixed and Neumann Boundary Conditions

In the experimental fluid dynamics community, there is an ongoing effort to improve on current methods and develop new ones to estimate pressure field from Particle Image Velocimetry data. One of the dominant approaches involves solving the Pressure Poisson Equation. Whereas the majority of solutions rely on numerical methods, the focus of the current study is to solve this equation analytically for a set of problems with different boundary conditions. Mixed boundary conditions may be useful in an internal flow where pressure can be directly measured on two boundaries using transducers. The all-Neumann boundary condition case is more favorable for far-field pressure calculations where direct pressure measurements are not feasible. The all-Dirichlet boundary condition case was not considered since it would require knowledge of pressure on the boundaries, which is usually the objective of the solution. All solutions were validated by calculating pressure of a Hill's vortex and comparing analytical results to the well-documented theoretical expression. Following the validation, solutions were applied to the Particle Image Velocimetry dataset of a flow containing a self-propelled vortex.