A dynamic regularized gradient model of the subgrid-scale scalar flux for large eddy simulations

Accurate predictions of scalar fields advected by a turbulent flow is needed for various industrial and geophysical applications. In the framework of large-eddy simulation (LES), a subgrid-scale (SGS) model for the subgrid-scale scalar flux has to be used. The gradient model (GM), which is derived from a Taylor series expansions of the filtering operation, is a well-known approach to model SGS scalar fluxes. This model is known to lead to high correlation level with the SGS scalar flux. However, this type of model cannot be used in practical LES because it does not lead to enough global scalar variance transfer from the large to the small scales. In this work, a regularization of the GM is proposed based on a physical interpretation of this model. The impact of the resolved velocity field on the resolved scalar gradient is decomposed into compressional, stretching, and rotational effects. It is shown that rotational effect is not associated with transfers of variance across scales. Conversely, the compressional effect is shown to lead to forward transfer, whereas the stretching effect leads to back-scatter of scalar variance. The proposed regularization is to neglect the stretching effect in the model formulation. The accuracy of this regularized gradient model (RGM) is tested in comparison with direct numerical simulations and compared with other classic SGS models. The accuracy of the RGM is evaluated in term of structural and functional performances, i.e., the model ability to locally approximate the SGS unknown term and to reproduce its global effect on tracer variance, respectively. It is found that the RGM associated with a dynamic procedure exhibits good performances in comparison with the standard dynamic eddy diffusivity model and the standard gradient model. In particular, the dynamic regularized gradient model (DRGM) provides a better prediction of scalar variance transfers than the standard gradient model. The DRGM is then evaluated in a series of large-eddy simulations. This shows a substantial improvement for various scalar statistics predictions.