Efficient and accurate data-driven wall modelling strategy for Reynolds averaged Navier–Stokes simulations

This article introduces a novel data-driven wall modeling strategy for Reynolds-Averaged Navier- Stokes (RANS) simulations. The method reformulates wall laws as a Dirichlet-to-Neumann map applied at a specific height within the boundary layer. This map is learned using neural networks trained on data from wall-resolved RANS simulations. While the approach shares similarities with the work of Romanelli et al. [1], it is significantly faster, as it eliminates the need for iterative resolution of the skin friction inherent in the implicit relation u + = f ( y + , p + ) . The model’s accuracy has also been improved through enhanced treatment of the turbulent variables and by incorporating additional input parameters that better describe the boundary layer state. The method is demonstrated on attached turbulent flows across various Reynolds numbers and wall pressure gradients. After training the neural networks on a subset of reference cases, their ability to generalize to both familiar and unseen conditions is evaluated. The model is further validated on a completely different setup (an airfoil), where it is compared to two existing analytical wall models, showing better accuracy and robustness with respect to pressure gradient conditions. The paper also introduces an efficient extrapolation-detection algorithm that could be used either to ensure that the model is always applied within its validity domain or to trigger an automated adaptive learning strategy of the wall-law or, in a zonal context, to select between wall-resolved/wall-modeled regions. Overall, our method provides a new practical intermediate-fidelity, cost-effective framework that displays an attractive balance between accuracy and computational efficiency, bridging the gap between the more computationally intensive approach of Romanelli et al. [1] and the limited accuracy of conventional analytical wall models.