A multigrid/ensemble Kalman Filter strategy for assimilation of unsteady flows

Abstract

A sequential estimator based on the Ensemble Kalman Filter for Data Assimilation of fluid flows is presented in this research work. The main feature of this estimator is that the Kalman filter update, which relies on the determination of the Kalman gain, is performed exploiting the algorithmic features of the numerical solver employed as a model. More precisely, the multilevel resolution associated with the multigrid iterative approach for time advancement is used to generate several low-resolution numerical simulations. These results are used as ensemble members to determine the correction via Kalman filter, which is then projected on the high-resolution grid to correct a single simulation which corresponds to the numerical model. The assessment of the method is performed via the analysis of one-dimensional and two-dimensional test cases, using different dynamic equations. The results show an efficient trade-off in terms of accuracy and computational costs required. In addition, a physical regularization of the flow, which is not granted by classical KF approaches, is naturally obtained owing to the multigrid iterative calculations. The algorithm is also well suited for the analysis of unsteady phenomena and, in particular, for potential application to in-streaming Data Assimilation techniques.

Assimilation of disparate data for enhanced reconstruction of turbulent mean flows

“…These approaches have been extensively used in weather forecasting and in geoscience. In addition, recently a multi-grid ensemble Kalman filter strategy [44] has been proposed to facilitate the efficient data assimilation for unsteady flows. It is achieved by using the ensemble of realizations from low resolution simulations to generate the Kalman correction and then projecting on high-resolution grids to correct the flow state.…”