Collaborative Research: CDS&E: Generalizable RANS Turbulence Models through Scientific Multi-Agent Reinforcement Learning

Reliable, predictive computational simulations of turbulent flows are essential for the advancement of key technologies in sectors ranging from aerospace and automotive to power generation. However, the utility of currently available simulations is limited, sometimes severely, by the unreliability of turbulence models. The most common computations of turbulence are intended to simulate only the mean or average velocity, with the effects of turbulence modeled, because in many applications this is the primary quantity of interest. However, the deployed models of turbulence are widely recognized as having limited reliability for complex flows of technological interest. The core reason for this challenge is the lack of universally applicable closure terms. This project addresses this shortcoming by formulating turbulence models to account for a more general description of the characteristics of the turbulence. This will yield models that are generally applicable, including complex turbulent flows. It will also yield technological advances in many important domains, including aeronautics, propulsion, power generation and wind energy that are presently hindered by the lack of reliable models of complex, turbulent flows. By developing reliable, predictive, and broadly applicable turbulence models, this project will have profound impacts on these fields, with the potential of enabling ground-breaking improvements in technologies important to our country and society. The objective of the project is to develop reliable Reynolds averaged Navier-Stokes models that generalize to complex turbulent flows. The approach is based on the hypothesis that current turbulence models do not retain a sufficiently rich representation of the statistical state of turbulence. A set of structure tensors that characterize the anisotropy and inhomogeneity of turbulence are proposed as a candidate for a sufficient statistical turbulence state space. Evolution equations for these structure tensors will be developed which will necessarily include unknown scalar functions of scalar invariants. These functions will be learned from turbulence statistical data using scientific multi-agent reinforcement learning. The required data will be obtained from direct numerical simulations and experiments. Models resulting from this process will be tested on a variety of complex turbulent flows. The potential impact of reliable Reynolds averaged turbulence models is hard to over-state, as they would greatly increase the value of computational fluid dynamics as a tool of science and engineering. In addition, the training of two graduate students under this project in the development of mathematical and data-informed models for complex systems will contribute to the highly skilled workforce required to address a broad class of complex problems facing our country and the world. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.