Physics-based localization methodology for Data Assimilation by Ensemble Kalman Filter

A physics-based methodology for the determination of the localization function for the Ensemble Kalman Filter (EnKF) is proposed. The spatial features of such function evolve dynamically over time according to the relevant instantaneous flow features of the ensemble members with the objective, to reduce the computational cost of the Data Assimilation (DA) procedure when applied with solvers for Computational Fluid Dynamics (CFD). The validation of the methodology has been carried out by the analysis of two test cases exhibiting different features. This permits to investigate different physical features, tailored for each test case, which affect the localization function. The flow over a two-dimensional square cylinder at $Re=150$ is the first case investigated. It has been shown that the proposed localization procedure leads to a more cost-effective DA process by reducing the size of the assimilated regions while keeping the same level of accuracy. The capabilities of the methodology are further demonstrated by the investigation of the turbulent flow around a three-dimensional circular cylinder for $Re=3900$. Again, the methodology exhibits an excellent trade off in terms of accuracy versus computational requirements.