A RANS approach to the Meshless Computation of Pressure Fields From Image Velocimetry

We propose a 3D meshless method to compute mean pressure fields in turbulent flows from image velocimetry. The method is an extension of the constrained Radial Basis Function (RBF) formulation by \citet{Sperotto2022} to a Reynolds Averaged Navier Stokes (RANS) framework. This is designed to handle both scattered data as in Particle Tracking Velocimetry (PTV) and data in uniform grids as in correlation-based Particle Image Velocimetry (PIV). The RANS extension includes the Reynolds stresses into the constrained least square problem. We test the approach on a numerical database featuring a Backward Facing Step (BFS) with a Reynolds number of 6400 (defined with respect to the inlet velocity and step height), obtained via Direct Numerical Simulation (DNS).