Previous studies have demonstrated that the Ensemble Kalman Filter (EnKF) has been successfully applied to optimize turbulence model constants under various flow conditions, particularly in two-dimensional cases. However, in engineering applications, the flow fields are often three-dimensional and highly nonlinear. Under such conditions, due to the non-uniqueness of the optimal solution in the inverse problem, directly applying the conventional EnKF often yields unsatisfactory results. To address this challenge, this study combines proper orthogonal decomposition (POD) with EnKF to develop a POD-reduced EnKF algorithm for data assimilation in complex three-dimensional flow fields of high-speed trains. By extracting flow field characteristics through POD, the number of observation points is reduced, which significantly enhances the data assimilation accuracy. Results show that the assimilated turbulence model constants lead to good agreement between simulation and experimental data for a high-speed train operating in open-air conditions. The method also demonstrates strong robustness, achieving consistent assimilation performance across different numbers and locations of observation points. In addition, the optimized constants exhibit a certain degree of generalizability, improving prediction accuracy across different inflow conditions and geometries. The proposed framework offers a promising strategy for enhancing aerodynamic modeling of high-speed trains.
Wang et al. (Sun,) studied this question.