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 Sperotto et al. (2022) 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).