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

Abstract

International audienceAccurate 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, 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 can not 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 gradient model 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 is tested in comparison with direct numerical simulations (DNS) and compared with other classic SGS models. The accuracy of the regularized gradient model 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 regularized gradient model 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 provides a better prediction of scalar variance transfers than the standard gradient model. The dynamic regularized gradient model is then evaluated in a series of large-eddy simulations. This shows a substantial improvement for various scalar statistics predictions

Extension of the subgrid-scale gradient model for compressible magnetohydrodynamics turbulent instabilities

“…The gradient (or non-linear) model 19,[21][22][23][24][25]34,55 arises from the analytical Taylor expansion of the SFS terms appearing in the MHD equations, under the hypothesis of having a filter with a Gaussian kernel. In the space domain this kernel can be written as…”

“…Comparisons between them have been studied in a variety of scenarios. [19][20][21] In this paper, we focus on the gradient model 19,[21][22][23][24][25] , based on a mathematical formulation which relates the finite resolution to an effective filtering of the equations. By expanding the filtered non-linear terms up to the first order of the Taylor series, one can approximate the residuals appearing in a given evolution equation with a functional form which includes the derivatives of the resolved fields, thus effectively extrapolating to the SGS the trends seen at the smallest resolved scales.…”

Space-Time Correlations and Dynamic Coupling in Turbulent Flows

“…Another approach is to use structural SGS models (Clark et al 1979, Bardina et al 1980, Stolz & Adams 1999, Domaradzki & Adams 2002, which are based on reconstructing the SGS stress to account for backscattering effects. Balarac et al (2013) developed a dynamic regularized gradient model, which is able to better predict space-time correlations compared with eddy-viscosity SGS models and gradient SGS models.…”

A nonlinear structural subgrid-scale closure for compressible MHD. I. Derivation and energy dissipation properties

“…In particular, it is a self-consistent extension of the YeoBedford (YB) expansions 1,31 as applied to compressible MHD. Closures of this family have been recently applied to incompressible [32][33][34] and compressible (supersonic) MHD 23,27 turbulence with encouraging results. The same method has also been used to model the transport of a passive scalar 34 .…”

“…Closures of this family have been recently applied to incompressible [32][33][34] and compressible (supersonic) MHD 23,27 turbulence with encouraging results. The same method has also been used to model the transport of a passive scalar 34 . Here, we focus on the closure derivation and extend it to include so far unaccounted for compressibility effects.…”