Data-driven turbulence modeling: A mutually coupled framework for symbolic regression and data assimilation

In recent years, machine learning techniques have demonstrated significant potential in the field of turbulence modeling. Symbolic regression, a white-box machine learning technique, offers a new approach to turbulence modeling by uncovering mathematical relationships within data and producing physically interpretable expressions. However, existing methods, which apply symbolic regression to white-box turbulence models through steady-state solutions, generally encounter convergence and stability issues during the posterior process of mutual coupling with the Reynolds-averaged Navier-Stokes (RANS) governing equations. In this study, turbulence modeling was mutually coupled based on the integration of symbolic regression and data assimilation. Initially, the model framework was constructed with high-confidence steady-state flow data. Subsequently, the undetermined parameters were identified by data assimilation techniques to enhance the accuracy of the white-box turbulence model. In this way, a precise white-box turbulence model was developed through mutual coupling with the RANS equations, so as to ensure consistency, stability, and convergence in the posterior flow field solutions. The results across various airfoils demonstrate that the mutually coupled data assimilation and symbolic regression model significantly reinforced the accuracy of simulating high Reynolds number flows with large-angle-of-attack separation compared to traditional RANS models. Furthermore, it exhibited robust stability and generalizability, offering a new framework for white-box turbulence modeling.