Enhancement of flow measurements using fluid-dynamic constraints

TL;DR

This paper introduces a novel filtering method that enhances noisy flow measurement data by reconstructing smooth, divergence-free velocity and pressure fields consistent with flow models, improving data quality for engineering and biological applications.

Contribution

The paper presents a new linear quadratic optimal control-based filter that effectively reduces noise in flow measurements while maintaining physical flow properties, with analysis and numerical validation.

Findings

Significant noise reduction in flow data

Improved accuracy of velocity and pressure fields

Outperforms existing smoothing methods

Abstract

Novel experimental modalities acquire spatially resolved velocity measurements for steady state and transient flows which are of interest for engineering and biological applications. One of the drawbacks of such high resolution velocity data is their susceptibility to measurement errors. In this paper, we propose a novel filtering strategy that allows enhancement of noisy measurements to obtain reconstruction of smooth divergence free velocity and corresponding pressure fields, which together approximately comply to a prescribed flow model. The main step in our approach consists of the appropriate use of the velocity measurements in the design of a linearized flow model which can be shown to be well-posed and consistent with the true velocity and pressure fields up to measurement and modeling errors. The reconstruction procedure is formulated as a linear quadratic optimal control problem and the resulting filter has analyzable smoothing and approximation properties. We also discuss briefly the discretization of our approach by finite element methods and comment on the efficient solution of the linear optimality system by iterative solvers. The capability of the proposed method to significantly reduce data noise is demonstrated by numerical tests in which we also compare to other methods like smoothing and solenoidal filtering.