Quantifying Numerical Uncertainty in Background-Oriented Schlieren

Our study presents and evaluates a method for computing the numerical uncertainty in Background Oriented Schlieren (BOS). We use Richardson extrapolation to assess the uncertainty of numerical integration of density gradients, based on residuals of density results across two grid levels. By integrating this numerical uncertainty with the existing random uncertainty, we obtain the final uncertainty of the density field. We assess the method's effectiveness using synthetic fields with artificial noise. Our error analysis shows that the sharpness of the density gradient significantly affects bias error and the prediction of numerical uncertainty. The prediction of numerical uncertainty corresponds to variations in bias error, particularly when the noise level and wavelength of the flow field are altered. By accounting for the numerical uncertainty, our method achieves up to 91% accuracy in predicting total uncertainty, as measured against the root-mean-square of the total error. We further demonstrate the utility of our methodology by applying it to experimental BOS images. Our proposed approach offers a more accurate understanding of uncertainty estimation in the BOS technique, with implications for future experiments.