Error propagation dynamics of velocimetry-based pressure field calculations (2): on the error profile

Abstract

This work investigates the propagation of error in a Velocimetry-based Pressure field reconstruction (VPressure) problem to determine and explain the effects of error profile of the data on the error propagation. The results discussed are an extension to those found in Pan et al. (2016). We first show how to determine the upper bound of the error in the pressure field, and that this worst scenario for error in the data field is unique and depends on the characteristics of the domain. We then show that the error propagation for a V-Pressure problem is analogous to elastic deformation in, for example, a Euler-Bernoulli beam or Kirchhoff-Love plate for one- and two-dimensional problems, respectively. Finally, we discuss the difference in error propagation near Dirichlet and Neumann boundary conditions, and explain the behavior using Green’s function and the solid mechanics analogy. The methods discussed in this paper will benefit the community in two ways: i) to give experimentalists intuitive and quantitative insights to design tests that minimize error propagation for a V-pressure problem, and ii) to create tests with significant error propagation for the benchmarking of V-Pressure solvers or algorithms. This paper is intended as a summary of recent research conducted by the authors, whereas the full work has been recently published (Faiella et al., 2021).