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We propose a meshless method to compute pressure fields from imagevelocimetry data, regardless of whether this is available on a regular grid asin cross-correlation based velocimetry or on scattered points as in trackingvelocimetry. The proposed approach is based on Radial Basis Functions (RBFs)regression and relies on the solution of two constrained least square problems.The first one is the regression of the measurements to create an analyticrepresentation of the velocity field. This regression can be constrained toimpose boundary conditions (e.g. no-slip velocity on a wall or inletconditions) or differential constraints (e.g. the solenoidal condition for anincompressible flow). The second one is the meshless integration of thepressure Poisson equation, achieved by seeking a solution in the form of a RBFexpansion and using constraints to impose boundary conditions.  We first illustrate the derivation of the two least square problems and thenumerical techniques implemented for their solution. Then, we showcase themethod with three numerical test cases of growing complexity. These are a 2DGaussian Vortex, a 2D flow past a cylinder from CFD and a 3D Stokes flow past asphere. For each case, we consider randomly sampled vector fields simulatingparticle tracking measurements and analyze the sensitivity to noise and seedingdensity.

A Meshless Method to Compute Pressure Fields from Image Velocimetry