Data assimilation for POD reduced-order model ?? Comparison of PF and EnKF

An integrated method of a proper orthogonal decomposition (POD) based reduced-order model (ROM) and data assimilation is proposed for real-time prediction of an unsteady flow field. In this paper, a particle filter (PF) and an ensemble Kalman filter (EnKF) are employed for data assimilation and the difference of predicted flow fields is evaluated in detail. The proposed method is validated using identical twin experiments of an unsteady flow field around a circular cylinder at Reynolds number of 1000. The PF and EnKF are employed to estimate coefficients of the ROM based on observed velocity components in the wake of the circular cylinder. The proposed method reproduces the unsteady flow field several orders faster than the reference numerical simulation based on Navier-Stokes equations. Furthermore, the prediction accuracy of ROM-PF is significantly better than that of ROM-EnKF. It is due to the flexibility of PF for representing a predictive probability density function compared to EnKF.