Wall-modeling of turbulent flows over a periodic hill using multi-agent reinforcement learning

A wall model for large-eddy simulation (LES) that can adapt to various pressure-gradient effects is developed for turbulent flow over a periodic hill using multi-agent reinforcement learning. A finite-volume unstructured incompressible LES solver is coupled with an open-source reinforcement learning tool to enable reinforcement learning in flow over complex geometries. In the training process, we simulate low-Reynolds-number flow over a periodic hill with reinforcement learning agents distributed on the wall of periodic hill, along the computational grid points. Each agent receives states based on local instantaneous flow quantities and a reward based on the estimated wall-shear stress, then provides local actions to update the wall boundary condition at each time step. The agents infer a single optimized policy through their repeated interactions with the flow field to maximize its cumulative long-term reward. The trained wall model is validated in higher-Reynolds-number simulations of the periodic hill configuration, and the results show the robustness of the model on flow with pressure gradients.