Optimized parametric inference for the inner loop of the Multigrid Ensemble Kalman Filter

TL;DR

This paper investigates the inner loop of the Multigrid Ensemble Kalman Filter, demonstrating its critical role in improving flow reconstruction accuracy and parametric optimization in fluid flow data assimilation.

Contribution

It introduces an optimized parametric inference method for the inner loop of the Multigrid Ensemble Kalman Filter, enhancing its performance for fluid flow data assimilation.

Findings

Inner loop significantly improves flow reconstruction accuracy.

Optimized inference enhances parametric estimation.

Results applicable to complex fluid flow models like LES.

Abstract

Essential features of the Multigrid Ensemble Kalman Filter (G. Moldovan, G. Lehnasch, L. Cordier, M. Meldi, A multigrid/ensemble Kalman filter strategy for assimilation of unsteady flows, Journal of Computational Physics 443-110481) recently proposed for Data Assimilation of fluid flows are investigated and assessed in this article. The analysis is focused on the improvement in performance due to the inner loop. In this step, data from solutions calculated on the higher resolution levels of the multigrid approach are used as surrogate observations to improve the model prediction on the coarsest levels of the grid. The latter represents the level of resolution used to run the ensemble members for global Data Assimilation. The method is tested over two classical one-dimensional problems, namely the linear advection problem and the Burgers' equation. The analyses encompass a number of different aspects, such as different grid resolutions. The results indicate that the contribution of the inner loop is essential in obtaining accurate flow reconstruction and global parametric optimization. These findings open exciting perspectives of application to grid-dependent reduced-order models extensively used in fluid mechanics applications for complex flows, such as Large Eddy Simulation (LES).