A Priori Tensor Basis Coefficients for Practical Turbulence Modeling via Weighted Regularization

A major class of machine learning-based turbulence models operates by predicting the coefficients of the tensor basis expansion. Previous investigations of the optimal tensor basis use only simplified flow with limited consideration of realistic model properties---sparsity, smoothness, and maximal non-negativity eddy viscosity. Here, these shortcomings are addressed by combining an optimal eddy viscosity with a novel alignment-weighted regularization (AWR) approach that focuses the regularization on highly aligned terms. The AWR approach is tuned and validated on square duct flow data, then used to investigate the Kawai Labs side-wall interference flow dataset, a complex 3D case exhibiting flow separation influenced by secondary motions. The key finding is that significantly higher accuracy can be obtained in the side-wall interference flow case than in the square duct case for the same regularization strength, with overall R² values of R² = 0.9979 and R² = 0.9811, respectively. These results indicate that requiring smooth coefficient fields imposes a stricter limit on accuracy than previously believed, depending on the case. The methodology developed here can be used to calculate tensor basis coefficients for training and establish more realistic limits to contextualize model performance.