We develop a wall model for large-eddy simulation (LES) that takes into account various pressure-gradient effects using multi-agent reinforcement learning. The model is trained using low-Reynolds-number flow over periodic hills with agents distributed on the wall at various computational grid points. It utilizes a wall eddy-viscosity formulation as the boundary condition to apply the modeled wall shear stress. Each agent receives states based on local instantaneous flow quantities at an off-wall location, computes a reward based on the estimated wall-shear stress, and provides an action to update the wall eddy viscosity at each time step. The trained wall model is validated in wall-modeled LES of flow over periodic hills at higher Reynolds numbers, and the results show the effectiveness of the model on flow with pressure gradients. The analysis of the trained model indicates that the model is capable of distinguishing between the various pressure gradient regimes present in the flow. To further assess the robustness of the developed wall model, simulations of flow over the Boeing Gaussian bump are conducted at a Reynolds number of 2 million, based on the free-stream velocity and the bump width. The results of mean skin friction and pressure on the bump surface, as well as the velocity statistics of the flow field, are compared to those obtained from equilibrium wall model (EQWM) simulations and published experimental data sets. The developed wall model is found to successfully capture the acceleration and deceleration of the turbulent boundary layer on the bump surface, providing better predictions of skin friction near the bump peak and exhibiting comparable performance to the EQWM with respect to the wall pressure and velocity field. We also conclude that the subgrid-scale model is crucial to the accurate prediction of the flow field, in particular the prediction of separation.
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This content will become publicly available on June 1, 2025
Sensitivity analysis of wall-modeled large-eddy simulation for separated turbulent flow
In this study, we conduct a parametric analysis to evaluate the sensitivities of wall-modeled
large-eddy simulation (LES) with respect to subgrid-scale (SGS) models, mesh resolution, wall
boundary conditions and mesh anisotropy. While such investigations have been conducted for
attached/flat-plate flow configurations, systematic studies specifically targeting turbulent flows
with separation are notably sparse. To bridge this gap, our study focuses on the flow over a
two-dimensional Gaussian-shaped bump at a moderately high Reynolds number, which involves
smooth-body separation of a turbulent boundary layer under pressure-gradient and surface-
curvature effects. In the simulations, the no-slip condition at the wall is replaced by three different
forms of boundary condition based on the thin boundary layer equations and the mean wall-shear
stress from high-fidelity numerical simulation to avoid the additional complexity of modeling the
wall-shear stress. Various statistics, including the mean separation bubble size, mean velocity
profile, and dissipation from SGS model, are compared and analyzed. The results reveal that
capturing the separation bubble strongly depends on the choice of SGS model. While simulations
approach grid convergence with resolutions nearing those of wall-resolved LES meshes, above this
limit, the LES predictions exhibit intricate sensitivities to mesh resolution. Furthermore, both wall
boundary conditions and the anisotropy of mesh cells exert discernible impacts on the turbulent
flow predictions, yet the magnitudes of these impacts vary based on the specific SGS model chosen
for the simulation.
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- Award ID(s):
- 2152705
- NSF-PAR ID:
- 10498044
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of Computational Physics
- Volume:
- 506
- Issue:
- C
- ISSN:
- 0021-9991
- Page Range / eLocation ID:
- 112948
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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