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 eddy viscosity from SGS model, are compared and analyzed. The results reveal that capturing the separation bubble strongly depends on the choice of SGS model. While grid convergence can be achieved at a resolution comparable to wall-resolved LES mesh, 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

Scientific multi-agent reinforcement learning for wall-models of turbulent flows

The predictive capabilities of turbulent flow simulations, critical for aerodynamic design and weather prediction, hinge on the choice of turbulence models. The abundance of data from experiments and simulations and the advent of machine learning have provided a boost to these modeling efforts. However, simulations of turbulent flows remain hindered by the inability of heuristics and supervised learning to model the near-wall dynamics. We address this challenge by introducing scientific multi-agent reinforcement learning (SciMARL) for the discovery of wall models for large-eddy simulations (LES). In SciMARL, discretization points act also as cooperating agents that learn to supply the LES closure model. The agents self-learn using limited data and generalize to extreme Reynolds numbers and previously unseen geometries. The present simulations reduce by several orders of magnitude the computational cost over fully-resolved simulations while reproducing key flow quantities. We believe that SciMARL creates new capabilities for the simulation of turbulent flows

Wall Modeling of Turbulent Flows with Various Pressure Gradients Using Multi-Agent Reinforcement Learning

We propose a framework for developing wall models for large-eddy simulation that is able to capture pressure-gradient effects using multi-agent reinforcement learning. Within this framework, the distributed reinforcement learning agents receive off-wall environmental states including pressure gradient and turbulence strain rate, ensuring adaptability to a wide range of flows characterized by pressure-gradient effects and separations. Based on these states, the agents determine an action to adjust the wall eddy viscosity, and consequently the wall-shear stress. The model training is in-situ with wall-modeled large-eddy simulation grid resolutions and does not rely on the instantaneous velocity fields from high-fidelity simulations. Throughout the training, the agents compute rewards from the relative error in the estimated wall-shear stress, which allows the agents to refine an optimal control policy that minimizes prediction errors. Employing this framework, wall models are trained for two distinct subgrid-scale models using low-Reynolds-number flow over periodic hills. These models are validated through simulations of flows over periodic hills at higher Reynolds numbers and flow over the Boeing Gaussian bump. The developed wall models successfully capture the acceleration and deceleration of wall-bounded turbulent flows under pressure gradients and outperform the equilibrium wall model in predicting skin friction.Comment: arXiv admin note: substantial text overlap with arXiv:2211.1642

Characterization of vortex regeneration mechanism in the self-sustaining process of wall-bounded flows using resolvent analysis

The regeneration mechanism of streamwise vortical structures in the self-sustaining process of wall-bounded turbulence is investigated. Resolvent analysis [1] is used to identify the principal forcing mode which produces the maximum amplification of the response modes in the minimal channel for the buffer [2] and logarithmic layer [3]. The identified mode is then projected out from the nonlinear term of the Navier-Stokes equations at each time step from the direct numerical simulations (DNS) of the corresponding minimal channel. The results show that the removal of the principal forcing mode is able to significantly inhibit turbulence for the buffer and logarithmic layer while removing the subsequent modes instead of the principal one only marginally affects the flow. Analysis of the dyadic interactions in the nonlinear term shows that the contributions toward the principal forcing mode come from a limited number of wavenumber interactions. Using conditional averaging, the flow structures that are responsible for generating the principal forcing mode, and thus the nonlinear interaction to self-sustain turbulence, are identified to be spanwise rolls interacting with meandering streaks