Realisability-informed machine learning for turbulence anisotropy mappings

Within the context of machine learning-based closure mappings for Reynolds-averaged Navier Stokes turbulence modelling, physical realisability is often enforced using ad hoc postprocessing of the predicted anisotropy tensor. In this study, we address the realisability issue via a new physics-based loss function that penalises non-realisable results during training, thereby embedding a preference for realisable predictions into the model. Additionally, we propose a new framework for data-driven turbulence modelling which retains the stability and conditioning of optimal eddy viscosity-based approaches while embedding equivariance. Several modifications to the tensor basis neural network to enhance training and testing stability are proposed. We demonstrate the conditioning, stability and generalisation of the new framework and model architecture on three flows: flow over a flat plate, flow over periodic hills and flow through a square duct. The realisability-informed loss function is demonstrated to significantly increase the number of realisable predictions made by the model when generalising to a new flow configuration. Altogether, the proposed framework enables the training of stable and equivariant anisotropy mappings, with more physically realisable predictions on new data. We make our code available for use and modification by others. Moreover, as part of this study, we explore the applicability of Kolmogorov–Arnold networks to turbulence modelling, assessing its potential to address nonlinear mappings in the anisotropy tensor predictions and demonstrating promising results for the flat plate case.