Non-Linear Super-Stencils for RANS turbulence model corrections

Turbulent flows occur across a wide range of scientific disciplines and engineering applications, yet remain challenging to predict computationally. This stems from the gap between highly expensive direct numerical simulations (DNS) and the inherent modeling errors of traditional Reynolds-Averaged Navier-Stokes (RANS) approaches.

Here, we introduce the Non-Linear Super-Stencil (NLSS)—a compact stencil that samples local mean flow features and maps them to a corrective force term using a fully connected neural network. Applied to the standard k-ω turbulence model, the NLSS correction achieves significant improvements in prediction accuracy across a family of periodic hill cases after training on a single reference case.

We demonstrate generalization across Reynolds numbers spanning 5600-19000 and geometric variations including different domain lengths and hill stretch factors. We attribute this to our physically-informed normalization procedure: stencils are aligned with local mean velocity, scaled by integral turbulent length scale, and both inputs and outputs are nondimensionalized and Galilean-transformed to the stencil's reference frame. These transformations embed physical invariants outside the neural network, reducing the complexity of the learned mapping.

Our results show that NLSS-corrected RANS solvers can generalize within flow families, nearing the accuracy of averaged DNS at much lower computational cost. Exploring different flow families is subject of ongoing work.