Fast estimation of pressure from PTV measurements using smooth particle hydrodynamics

Estimation of pressure fields from particle tracking velocimetry (PTV) techniques such Shake-The-Box (STB) remains challenging. Traditional methods such VIC, FLOWFIT, etc. involve the estimation of Eulerian flows fields from measured Lagrangian particle tracks subject to physical constraints. These methods are memory intensive and potentially introduce averaging errors. In this work, we propose a purely Lagrangian approach to compute instantaneous pressure from PTV using discretization based on smooth particle hydrodynamics (SPH). Pressure is obtained via a linear system that enforces the full Navier-Stokes equations. We use Voronoi tessellation on the particle field to obtain local volumes and efficiently identify nearest neighbors. A comparison with other neighbor detection approach is also reported. This framework does not require special treatment at measurement boundaries and is verified and validated using a model problem of a Taylor--Green vortex and analysed on a canonical 3D flow past the cylinder at moderate Reynolds numbers. Computational cost, convergence, and challenges are reported.