Utilizing ensemble Kalman filtering in proper orthogonal decomposition Galerkin reduced-order models for turbulent flow prediction

Developing reduced-order models for turbulent flow prediction is essential for engineering applications. This research introduces a reduced-order model based on the ensemble Kalman filter (EnKF) approach, designed to refine the ordinary differential equation constants in proper orthogonal decomposition Galerkin (POD-Galerkin) reduced-order models using time coefficient constraints. The model's predictive capability is validated with two cases: flow around a cylinder and flow around a wall-mounted hemisphere. Notably, the time coefficients of the POD-Galerkin model, updated with EnKF, showed high consistency with the original POD coefficients after several iterations, indicating enhanced prediction accuracy. The results revealed that only 17 iterations were required for the two-dimensional cylinder flow model to reduce the relative prediction error to below 1%. For the three-dimensional hemisphere flow case, the relative error was 2.03%, with the time coefficients' relative errors in various modes decreasing by one to two orders of magnitude compared to the traditional POD-Galerkin method. This approach effectively prevents divergence in low-order models over long time periods and provides a robust method for low-dimensional representation of high-fidelity flow fields.