Law-of-the-Wall-Constrained Model Augmentation Using Field Inverse and Machine Learning

We conduct a constrained recalibration of the Spalart-Allmaras (SA) model within the framework of field inversion and machine learning (FIML). Unlike conventional FIML, our approach imposes constraints to preserve the law of the wall (LoW), a key calibration of the baseline SA model, throughout the field inversion, machine learning steps, and subsequent implementation in a production CFD code. The baseline model is trained using periodic hill data. During validation, we observe that preserving the LoW is not essential for flow configurations similar to the training dataset but becomes critical for model generalization to configurations outside the training data. Preserving the LoW not only maintains the model’s performance in the plane channel flow and flat-plate boundary-layer flows but also enhances its generalizability to configurations where non-equilibrium effects dominate and the LoW appears irrelevant. Specifically, the constrained FIML approach provides more accurate predictions of separation bubble size in the backward-facing step case and improved skin friction predictions for the three-dimensional BeVERLI hill case—both of which are known to be challenging for RANS models. In contrast, unconstrained FIML performs worse and is comparable to the baseline SA model in these scenarios. These findings indicate that the lack of generalization in existing data-driven models is not inherently due to the FIML framework itself. More importantly, the results underscore the importance of preserving baseline model calibrations to ensure the generalizability of data-driven turbulence models.