Progressive augmentation of Reynolds stress tensor models for secondary flow prediction by computational fluid dynamics driven surrogate optimisation

Generalisability and the consistency of the a posteriori results are the most critical points of view regarding data-driven turbulence models. This study presents a progressive improvement of turbulence models using simulation-driven Bayesian optimisation with Kriging surrogates where the optimisation of the models is achieved by a multi-objective approach based on duct flow quantities. We aim for the augmentation of secondary-flow prediction capability in the linear eddy-viscosity model k-! SST without violating its original performance on canonical cases e.g. channel flow. Progressively data-augmented explicit algebraic Reynolds stress models (PDA-EARSMs) for k - ! SST are obtained enabling the prediction of secondary flows that the standard model fails to predict. The new models are tested on channel flow cases guaranteeing that they preserve the successful performance of the original k - ! SST model. Subsequently, numerical verification is performed for various test cases. Regarding the generalisability of the new models, results of unseen test cases demonstrate a significant improvement in the prediction of secondary flows and streamwise velocity. These results highlight the potential of the progressive approach to enhance the performance of data-driven turbulence models for fluid flow simulation while preserving the robustness and stability of the solver.