Abstract:

A robust, low-order POD-based state estimator, also known as an observer, for the challenging fluid-dynamics test-case of uncertain 2D Boussinesq equations is presented in this paper. The observer design is based on the methodology recently introduced by the authors1, which incorporates robustness to bounded model uncertainties, and data-driven auto-tuning of the observer gains. An extensive numerical study on the 2D Boussinesq equations with parametric uncertainties demonstrates the performance of our observer. The reported numerical results show that the proposed observer allows estimation of the complete temperature and velocity fields from a reduced number of measurements. It is also shown that the proposed observer is robust to changes or errors in the value of the Reynolds number. In other words, we show that we can design the observer based