Field inversion and machine learning based on the Rubber–Band Spalart–Allmaras Model

• A new parametric relationship for the RBSA model is constructed to further protect the law-of-wall when the adjustable parameters of the RBSA take extreme value and facilitate the field inversion of the RBSA model. • The rubber-band Spalart–Allmaras (RBSA) model is coupled with the field inversion and machine learning method to construct data-driven turbulence model that does not harm the law-of-wall. • We confirmed that even if the adjustable parameter in the RBSA model is changed to functions of local flow features, the ability of the RBSA model to hold the law-of-wall still exists. Machine learning (ML) techniques have emerged as powerful tools for improving the predictive capabilities of Reynolds-averaged Navier–Stokes (RANS) turbulence models in separated flows. This improvement is achieved by leveraging complex ML models, such as those developed using field inversion and machine learning (FIML), to dynamically adjust the constants within the baseline RANS model. However, the ML models often overlook the fundamental calibrations of the RANS turbulence model. Consequently, the basic calibration of the baseline RANS model is disrupted, leading to a degradation in the accuracy, particularly in basic wall-attached flows outside of the training set. To address this issue, a modified version of the Spalart-Allmaras (SA) turbulence model, known as Rubber-band SA (RBSA), has been proposed recently. This modification involves identifying and embedding constraints related to basic wall-attached flows directly into the model. It is shown that no matter how the parameters of the RBSA model are adjusted as constants throughout the flow field, its accuracy in wall-attached flows remains unaffected. In this paper, we propose a new constraint for the RBSA model, which better safeguards the law of wall in extreme conditions where the model parameter is adjusted dramatically. The resultant model is called the RBSA-poly model. We then show that when combined with FIML augmentation, the RBSA-poly model effectively preserves the accuracy of simple wall-attached flows, even when the adjusted parameters become functions of local flow variables rather than constants. A comparative analysis with the FIML-augmented original SA model reveals that the augmented RBSA-poly model reduces error in basic wall-attached flows by 50% while maintaining comparable accuracy in trained separated flows. These findings confirm the effectiveness of utilizing FIML in conjunction with the RBSA model, offering superior accuracy retention in cardinal flows.