Optimal estimator and artificial neural network as efficient tools for the subgrid-scale scalar flux modeling

This work is devoted to exploring a new procedure to develop subgrid-scale (SGS) models in the context of large-eddy simulation (LES) of a passive scalar. Starting from the Noll’s formula (Noll 1967), the concept of an optimal estimator is first used to determine an accurate set of parameters to derive a SGS model. The SGS model is then defined as a surrogate model built from this set of parameters by training an artificial neural network (ANN) on a filtered DNS database. This ANN model is next compared with the dynamic nonlinear tensorial diffusivity (DNTD) model proposed by Wang et al. (2007). The DNTD model is also based on Noll’s formula and can be seen as a nonlinear extension of the dynamic eddy-diffusivity (DED) model proposed by Moin et al. (1991). The a priori and a posteriori tests performed on the ANN model demonstrate the ability of this new model to well reproduce the behavior of the exact SGS term and show an improvement in comparison with DED and DNTD models. The concept of an optimal estimator associated with a machine-learning procedure thus appears as a useful tool for SGS model development.