Non-Linear Super-Stencils for turbulence model corrections

Despite playing an important role across a wide range of scientific disciplines, the simulation of highly turbulent flows remains challenging. This is due to the gap between the often prohibitive computational cost of direct numerical simulation and the inherent modeling errors incurred by traditional Reynolds-Averaged Navier-Stokes (RANS) approaches. Data-driven turbulence models aim to close this gap by learning from high-fidelity data. Here, we introduce the Non-Linear Super-Stencil (NLSS), that is, a compact stencil sampling local mean flow features and mapping them to a corrective force term by employing a neural network. Applied to standard turbulence models, the NLSS correction significantly improves accuracy on a family of periodic hill cases (varying in Reynolds number and geometry) after training on a single case. We attribute this generalizability to our normalization and transformation procedure: The stencil is aligned with the local mean velocity and scaled by the local integral turbulent length scale, and both the model’s input features and output force are nondimensionalized and transformed to the stencil’s frame of reference. In summary, this work aims at NLSS-corrected RANS solvers able to generalize to a large class of turbulent flow problems, achieving the accuracy of averaged direct numerical simulation at much lower cost.