Data Assimilation for Transonic Flows Integrating Reduced-Order Models and Active Learning

Data assimilation has been widely used to integrate numerical simulation and experimental methods, the two primary approaches to investigate fluid dynamics, to improve flow predictions by reducing the uncertainties inherent in both methodologies. In this research, we employ data assimilation based on the ensemble Kalman filter to recover transonic flows over an airfoil and optimize the initial inflow parameters from sparse experimental measurements of the surface pressure coefficients. To improve computational efficiency, we develop a nonintrusive reduced-order model that utilizes proper orthogonal decomposition and kriging interpolation, effectively replacing the expensive numerical solver. In addition, we incorporate an active learning sampling method that ensures the accuracy of the reduced-order model as the assimilation process evolves. The proposed method is applied to transonic flows over a NACA 0012 airfoil, with weak and strong shock waves. The results indicate that the proposed approach improves the accuracy by nearly two orders of magnitude compared to assimilation solely based on the reduced-order model. Remarkably, this accuracy enhancement is complemented by a substantial reduction in computational cost, with the required time being only 15.43% of that for the assimilation process based entirely on the numerical solver.