A non-linear observer for unsteady three-dimensional flows

A method is proposed to estimate the velocity field of an unsteady flow using a limited number of flow measurements. The method is based on a non-linear low-dimensional model of the flow and on an expansion of the velocity field in terms of empirical basis functions. The main idea is to impose that the coefficients of the modal expansion of the velocity field gives the best approximation of the available measurements, while at the same time satisfying the non-linear low-order model as closely as possible. Practical applications may range from feedback flow control to the monitoring of the flow in non-accessible regions. The proposed technique is applied to the flow around a confined square cylinder, both in two- and three-dimensional flow regimes. Comparisons are provided with existing linear and non-linear estimation techniques.