Log-law recovery through reinforcement-learning wall model for large-eddy simulation

TL;DR

This paper introduces a reinforcement learning-based wall model for large-eddy simulation that effectively captures near-wall turbulence across a wide range of Reynolds numbers without relying on high-fidelity data.

Contribution

A novel RL wall model called VYBA23 is developed, trained on a single Reynolds number, and tested across eleven Reynolds numbers, demonstrating robustness and potential for physical law recovery.

Findings

Little effect on mean flow field

Some impact on wall-shear stress fluctuations

Effective across a wide Reynolds number range

Abstract

This paper focuses on the use of reinforcement learning (RL) as a machine-learning (ML) modeling tool for near-wall turbulence. RL has demonstrated its effectiveness in solving high-dimensional problems, especially in domains such as games. Despite its potential, RL is still not widely used for turbulence modeling and is primarily used for flow control and optimization purposes. A new RL wall model (WM) called VYBA23 is developed in this work, which uses agents dispersed in the flow near the wall. The model is trained on a single Reynolds number ($Re_\tau = 10^4$) and does not rely on high-fidelity data, as the back-propagation process is based on a reward rather than output error. The states of the RLWM, which are the representation of the environment by the agents, are normalized to remove dependence on the Reynolds number. The model is tested and compared to another RLWM (BK22) and to an equilibrium wall model, in a half-channel flow at eleven different Reynolds numbers ($Re_\tau \in [180;10^{10}]$). The effects of varying agents' parameters such as actions range, time-step, and spacing are also studied. The results are promising, showing little effect on the average flow field but some effect on wall-shear stress fluctuations and velocity fluctuations. This work offers positive prospects for developing RLWMs that can recover physical laws, and for extending this type of ML models to more complex flows in the future.