A reduced order Kalman Filter model for sequential Data Assimilation of turbulent flows

Abstract: A Kalman filter based sequential estimator is presented in the present work. The estimator is integrated in the structure of segregated solvers for the analysis of incompressible flows. This technique provides an augmented flow state integrating available observation in the CFD model, naturally preserving a zero-divergence condition for the velocity field. Because of the prohibitive costs associated with a complete Kalman Filter application, two model reduction strategies have been proposed and assessed. These strategies dramatically reduce the increase in computational costs of the model, which can be quantified in an increase of $10\% - 15\%$ with respect to the classical numerical simulation. In addition, an extended analysis of the behavior of the numerical model covariance $Q$ has been performed. The results have shown that optimized values are strongly linked to the truncation error of the discretization procedure. The estimator has been applied to the analysis of a number of test cases exhibiting increasing complexity, including turbulent flow configurations. The results show that the augmented flow successfully improves the prediction of the physical quantities investigated, even when the observation is provided in a limited region of the physical domain. In addition, the present work indicates that these Data Assimilation techniques, which are at an embryonic stage of development in CFD, can be pushed even further using the augmented prediction as a powerful tool for the optimization of the free parameters in the numerical simulation.