A physics embedded neural-network sub-grid-scale model for simulating flames in turbulence*

A neural network for large-eddy simulation (LES) of turbulent reacting flows is embedded in the governing equations as a sub-grid-scale closure. Its training is fully coupled with the physics of the filtered governing equations: the network parameters are optimized based on model-predicted observables, which entails coupling numerical solutions of the adjoint governing equations with the usual backpropagation training gradient. It is also designed to preserve mass fraction boundedness with a total variation diminishing (TVD) property. We demonstrate the method for a statistically planar premixed flame in isotropic turbulence with a single-species, single-step, and irreversible chemical reaction. It is trained to correct the short-time deviation from a spatially filtered solution of direct numerical simulation. The trained model is then applied to a longer LES and is evaluated based on predicted statistical quantities of interest. Finally, the trained model is demonstrated on the out-of-sample configuration of an expanding spherical flame in isotropic turbulence.