Computational optimization of omni-directional pressure integration schemes

Variations in the pressure field play an important role in many fluid dynamics problems. For turbulent flows in particular the pressure fluctuations and their correlations with the instantaneous velocity field are a major contributor to the evolution of the turbulent transport. However, measurement of fluctuating pressure is very difficult without resorting to invasive pressure probes, and the spatially resolved information needed for analysis of pressure gradient terms in the turbulent transport equations is generally not available through direct diagnostics. Instead, researchers have pursued calculation of pressure fields from experimentally measured velocity fields but multiple papers have shown that such calculations are very sensitive to propagation of experimental error. Various strategies have emerged to control this effect, with one of the most robust being the various omni-directional pressure integration schemes which are usually shown to minimize the resultant error on the pressure fields as compared to matrix inversion approaches such as Poisson equation solutions. Unfortunately, this technique, while tractable in 2D, can be significantly more expensive when adapted to 3D, which has been shown to be important for evaluating the true pressure fields. In this work we will propose and explore several options for optimizing omni-directional pressure integration methods for both 2- and 3D calculations by reducing or eliminating the need to explicitly calculate each individual line integral, and compare their effect on the accuracy and efficiency of the methods as compared to the original approach and Poisson solvers in various simulated and experimental flows.