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

TL;DR

This paper introduces a multigrid/ensemble Kalman filter method that leverages multilevel numerical simulations for efficient data assimilation in unsteady fluid flows, improving accuracy and computational efficiency.

Contribution

The novel approach integrates multigrid resolution with ensemble Kalman filtering, enabling efficient unsteady flow data assimilation with natural flow regularization.

Findings

Effective trade-off between accuracy and computational cost.

Natural physical regularization of flows through multigrid calculations.

Suitable for unsteady phenomena and streaming data assimilation.

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.