Error Propagation Dynamics of PIV-based Pressure Field Calculations: How well does the pressure Poisson solver perform inherently?

TL;DR

This paper analyzes how errors in PIV velocity measurements propagate through the pressure Poisson solver, revealing the influence of boundary conditions, domain size, and flow type on pressure calculation accuracy.

Contribution

It provides an analytical framework for understanding error propagation in PIV-based pressure calculations, which was previously underexplored.

Findings

Error propagation depends on boundary conditions and domain size.

The mathematical roots of error amplification are identified.

Error bounds are analytically quantified.

Abstract

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.