Real-time estimation of turbulent velocity fields using sparse sensor measurements

Abstract

The problem of predicting turbulent velocity fields using state-space models and sensor measurements in real time is addressed with a focus on direct and inverse problems of contaminant dispersion in urban areas. The concept of low dimensionality through the use of proper orthogonal decomposition (POD) is a key concept in the development of efficient models for data assimilation. An extension of POD called episodic-POD is developed for optimally combining state-space and measurement models. This assimilation method is shown to be robust to noise and allows one to approximate velocity fields at past and present instances in time simultaneously. The methods developed are numerically validated through various examples.