Accurate deep learning sub-grid scale models for large eddy simulations
Rikhi Bose Arunabha M. Roy
We present two families of sub-grid scale (SGS) turbulence models developed
for large-eddy simulation (LES) purposes. Their development required the
formulation of physics-informed robust and efficient Deep Learning (DL)
algorithms which, unlike state-of-the-art analytical modeling techniques can
produce high-order complex non-linear relations between inputs and outputs.
Explicit filtering of data from direct simulations of the canonical channel
flow at two friction Reynolds numbers $Re_\tau\approx 395$ and 590 provided
accurate data for training and testing. The two sets of models use different
network architectures. One of the architectures uses tensor basis neural
networks (TBNN) and embeds the simplified analytical model form of the general
effective-viscosity hypothesis, thus incorporating the Galilean, rotational and
reflectional invariances. The other architecture is that of a relatively simple
network, that is able to incorporate the Galilean invariance only. However,
this simpler architecture has better feature extraction capacity owing to its
ability to establish relations between and extract information from
cross-components of the integrity basis tensors and the SGS stresses. Both sets
of models are used to predict the SGS stresses for feature datasets generated
with different filter widths, and at different Reynolds numbers. It is shown
that due to the simpler model's better feature learning capabilities, it
outperforms the invariance embedded model in statistical performance metrics.
In a priori tests, both sets of models provide similar levels of dissipation
and backscatter. Based on the test results, both sets of models should be
usable in a posteriori actual LESs.