A Meshless Method to Compute Pressure Fields from Image Velocimetry

TL;DR

This paper introduces a meshless, RBF-based method to accurately compute pressure fields from image velocimetry data, applicable to both regular and scattered measurement points, with boundary and differential constraints.

Contribution

The novel approach combines RBF regression and meshless pressure integration, accommodating various data types and boundary conditions, advancing pressure field computation techniques.

Findings

Effective in 2D and 3D test cases

Robust to noise and seeding density variations

Applicable to diverse flow scenarios

Abstract

We propose a meshless method to compute pressure fields from image velocimetry data, regardless of whether this is available on a regular grid as in cross-correlation based velocimetry or on scattered points as in tracking velocimetry. 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 analytic representation of the velocity field. This regression can be constrained to impose boundary conditions (e.g. no-slip velocity on a wall or inlet conditions) or differential constraints (e.g. the solenoidal condition for an incompressible flow). The second one is the meshless integration of the pressure Poisson equation, achieved by seeking a solution in the form of a RBF expansion and using constraints to impose boundary conditions. We first illustrate the derivation of the two least square problems and the numerical techniques implemented for their solution. Then, we showcase the method with three numerical test cases of growing complexity. These are a 2D Gaussian Vortex, a 2D flow past a cylinder from CFD and a 3D Stokes flow past a sphere. For each case, we consider randomly sampled vector fields simulating particle tracking measurements and analyze the sensitivity to noise and seeding density.