# Quantitative Evaluation of a Linear Reduced-order Model based on Particle-image-velocimetry Data of Separated Flow Field around Airfoil

## TL;DR

This paper presents a quantitative evaluation method for linear reduced-order models of separated flow around an airfoil using PIV data, assessing model accuracy and predictability based on POD and DMD techniques.

## Contribution

It introduces a systematic evaluation approach for reduced-order flow models derived from PIV data, comparing different mode selections and estimation methods.

## Key findings

- Forward DMD modes yield the best model performance.
- Using 2-10 DMD modes optimizes model accuracy.
- Evaluation method effectively quantifies estimation error and predictability.

## Abstract

A quantitative evaluation method for a reduced-order model of the flow field around an NACA0015 airfoil based on particle image velocimetry (PIV) data is proposed in the present paper. The velocity field data obtained by the time-resolved PIV measurement were decomposed into significant modes by a proper orthogonal decomposition (POD) technique, and a linear reduced-order model was then constructed by the linear regression of the time advancement of the POD modes or the sparsity promoting dynamic mode decomposition (DMD). The present evaluation method can be used for the evaluation of the estimation error and the model predictability. The model was constructed using different numbers of POD or DMD modes for order reduction of the fluid data and different methods of estimating the linear coefficients, and the effects of these conditions on the model performance were quantitatively evaluated. The results illustrates that forward (standard) model works the best with two to ten significant DMD modes selected by sparsity promoting DMD.