Characteristic scales of Townsend's wall-attached eddies

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 turbulence 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 unprecedented capabilities for the simulation of turbulent flows.

Simulations of turbulent flows are relevant for aerodynamic and weather modeling, however challenging to capture flow dynamics in the near wall region. To solve this problem, the authors propose a multi-agent reinforcement learning approach to discover wall models for large-eddy simulations.

Effect of Wall Boundary Conditions on a Wall-Modeled Large-Eddy Simulation in a Finite-Difference Framework

We studied the effect of wall boundary conditions on the statistics in a wall-modeled large-eddy simulation (WMLES) of turbulent channel flows. Three different forms of the boundary condition based on the mean stress-balance equations were used to supply the correct mean wall shear stress for a wide range of Reynolds numbers and grid resolutions applicable to WMLES. In addition to the widely used Neumann boundary condition at the wall, we considered a case with a no-slip condition at the wall in which the wall stress was imposed by adjusting the value of the eddy viscosity at the wall. The results showed that the type of boundary condition utilized had an impact on the statistics (e.g., mean velocity profile and turbulence intensities) in the vicinity of the wall, especially at the first off-wall grid point. Augmenting the eddy viscosity at the wall resulted in improved predictions of statistics in the near-wall region, which should allow the use of information from the first off-wall grid point for wall models without additional spatial or temporal filtering. This boundary condition is easy to implement and provides a simple solution to the well-known log-layer mismatch in WMLES.

Error scaling of large-eddy simulation in the outer region of wall-bounded turbulence

We study the error scaling properties of large-eddy simulation (LES) in the outer region of wall-bounded turbulence at moderately high Reynolds numbers. In order to avoid the additional complexity of wall-modeling, we perform LES of turbulent channel flows in which the no-slip condition at the wall is replaced by a Neumann condition supplying the exact mean wall-stress. The statistics investigated are the mean velocity profile, turbulence intensities, and kinetic energy spectra. The errors follow( Δ / L ) α R e τ γ , where Δ is the characteristic grid resolution, Re τ is the friction Reynolds number, and L is the meaningful length-scale to normalize Δ in order to collapse the errors across the wall-normal distance. We show that Δ can be expressed as the L 2-norm of the grid vector and that L is well represented by the ratio of the friction velocity and mean shear. The exponent α is estimated from theoretical arguments for each statistical quantity of interest and shown to roughly match the values computed by numerical simulations. For the mean profile and kinetic energy spectra, α ≈ 1, whereas the turbulence intensities converge at a slower rate α < 1. The exponent γ is approximately 0, i.e. the LES solution is independent of the Reynolds number. The expected behavior of the turbulence intensities at high Reynolds numbers is also derived and shown to agree with the classic log-layer profiles for grid resolutions lying within the inertial range. Further examination of the LES turbulence intensities and spectra reveals that both quantities resemble their filtered counterparts from direct numerical simulation (DNS) data, but that the mechanism responsible for this similarity is related to the balance between the input power and dissipation rather than to filtering.