Physics-informed neural networks for the Reynolds-Averaged Navier-Stokes modeling of Rayleigh-Taylor turbulent mixing

Recently, Physics-informed neural networks (PINNs) have proven to be an efficient machine-learning method for solving partial differential equations. However, this method can be quite challenging when solving complex problems with shock/material discontinuities or multi-scale features, such as turbulence. In this paper, we propose an improved PINNs framework for solving the Reynolds-averaged Navier-Stokes (RANS) equations for turbulent mixing induced by the Rayleigh-Taylor (RT) instability. The RANS model is based on the closure form of the K-L model. However, the transport equations of the turbulent kinetic energy K and turbulent length scale L are not included and are instead predicted directly by neural networks, thus resulting in an inverse problem. Several modifications are made to the original PINNs to improve its applicability to RT turbulent mixing and accelerate the training optimization process. We first examine the applicability of the PINNs for solving multi-material Euler equations without considering turbulence. Then, PINNs is applied to the RT turbulent mixing problem using training data from the traditional K-L model. The results confirm the ability of the PINNs to predict the entire spatiotemporal field using limited training data. Next, we further train the PINNs using data from the implicit large eddy simulation (ILES), which yields a PINN-based turbulence model that performs better than the traditional K-L model. These results shed light on further applications of PINNs for complex problems, particularly those with limited measurement data and unknown physical models.