Mathematics

In this talk, a machine learning-based framework is introduced to enhance the generalizability of turbulence closures in Reynolds-Averaged Navier-Stokes (RANS) simulations. The framework is constructed upon a set of specialized "expert" models, trained using sparse Bayesian learning and symbolic regression for distinct flow regimes, including turbulent channel flows, separated boundary layers, and near-sonic axisymmetric jet. These expert models are blended intrusively within the RANS equations through spatially varying weighting functions. For example, such functions are derived using a Gaussian kernel applied to a reference dataset spanning equilibrium shear to separation-dominated flows. To enable predictions in unseen scenarios, a regressor, such as a Random Forests, is trained to map local physical features to the corresponding weights. The framework is assessed on both training and unseen test cases, covering flow configurations from fully attached boundary layers to near-stall conditions. Across these scenarios, the blended model is shown to adapt to local flow physics, selectively activating the most appropriate expert in each region.