Application of regularization to LES-informed data-driven turbulence model

Abstract

Abstract: This project evaluates the role of regularization in the data-driven augmentation of Reynolds-Averaged Navier–Stokes (RANS) turbulence models through field inversion, with particular emphasis on its implications for aerodynamic shape optimization. While field inversion techniques have demonstrated considerable potential in bridging the accuracy gap between RANS and high-fidelity simulations such as Large Eddy Simulation (LES), the inverse problem remains inherently ill-posed. To address this challenge, the Source-Transformed Adjoint Multi-Physics Solver (STAMPS) is extended to incorporate regularization mechanisms within its adjoint-based field inversion framework. The methodology involves introducing spatially varying correction factors into the Spalart–Allmaras turbulence model and optimizing them using gradients computed by the discrete adjoint. Different levels of Tikhonov-type regularization are applied, penalizing both the magnitude and variation of the correction fields to enforce smoothness and stability. The impact of the regularization parameter is systematically analyzed using the L-curve method, which balances fidelity to LES reference data against the smoothness of the correction field. This approach ensures that the learned model corrections not only reduce RANS–LES discrepancies but also remain physically consistent and robust for optimization workflows. Results demonstrate that properly calibrated regularization enhances the smoothness and interpretability of the correction fields without compromising predictive accuracy. Furthermore, the augmented model produces more reliable adjoint sensitivities, which are essential for gradient-based shape optimization. The findings underscore the significance of integrating regularization within data-driven turbulence modeling frameworks, thereby offering a pathway toward more stable and physically meaningful RANS augmentations suitable for industrial design applications.