Reynolds-averaged Navier-Stokes (RANS) turbulence models rely on several simplifying assumptions that limit their accuracy, particularly in predicting separated flows. To address these limitations, significant efforts have focused on augmenting RANS models through field inversion and machine learning. In the present study, data assimilation and symbolic regression are used to formulate an analytical correction to the Spalart-Allmaras model, addressing local deficiencies in its production term. A key objective of this work is to develop a correction applicable to a wide range of flow configurations, improving predictions for separated flows without degrading the performance of the baseline model for wall-attached flows. To this end, symbolic regression is performed using assimilated data from two-dimensional separated-flow cases (converging-diverging channel, bump H42, and NASA wall-mounted hump) together with a reference case where the Spalart-Allmaras model remains accurate (flat plate). This methodology enforces the desired correction in separated flows while minimizing the impact on the model's accuracy for wall-attached flows. The symbolic correction accurately reproduces the assimilated quantities and its performance on unseen flows demonstrates that the resulting expression remains applicable across a broad range of flow configurations and Reynolds numbers (bump H38, square cylinder, and periodic hill). The correction is also assessed on three-dimensional cases, namely, the FAITH hill and the Ahmed body. While improvements are observed for some configurations, these tests also reveal limitations that warrant further investigation.

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• Aerodynamics
• Turbulence
• Turbulence modeling