Implicit modeling of equivariant tensor basis with Euclidean turbulence closure neural network

Improved turbulence models are necessary for achieving more accurate solutions in Reynolds-averaged Navier–Stokes (RANS) simulations. RANS is widely used in various engineering applications, and enhancing its accuracy is crucial for geometry design and control applications. With the increasing availability of high-fidelity datasets, machine learning (ML) techniques offer the opportunity for data-driven inference of RANS equation closure terms. By Pope's theoretical analysis, ML turbulence closure models for RANS simulations are often used alongside physics-informed preprocessing of equivariant tensor basis. In this work, we replace this established approach by designing an equivariant turbulence model with Euclidean Neural Networks (e3nn). We demonstrate that Pope's tensor basis is a special case of our model. We test the model on the periodic hills flow case dataset. Our approach significantly improves the prediction of anisotropic components of Reynolds stresses, leading to more accurate modeling of the flow field when integrated into RANS through a single injection.