On a proper tensorial subgrid heat flux model for LES

Abstract

Abstract In this work, we aim to shed light on the following research question: can we find a subgrid-scale (SGS) heat flux model with good physical and numerical properties, such that we can obtain satisfactory predictions for buoyancy-driven turbulence at high Rayleigh numbers? This is motivated by our previous findings showing the limitations of existing SGS heat flux models for LES. On one hand, the most popular models rely on the eddy-diffusivity assumption despite their well-known lack of accuracy in a priori studies. On the other hand, the gradient model, which is the leading term of the Taylor series of the SGS flux, is much more accurate a priori but cannot be used as a standalone model since it produces a finite-time blow-up. In this context, we firstly aim to reconcile accuracy and stability for the gradient model. To do so, it is expressed as a linear combination of regularized (smoother) forms of the convective operator. The new alternative form can indeed be viewed as an approximate deconvolution of the exact SGS flux. Moreover, it facilitates the mathematical analysis of the gradient model, neatly identifying those terms that may cause numerical instabilities, leading to a new unconditionally stable non-linear model that can indeed be viewed as a stabilized version of the gradient model. In this way, we expect to combine the good a priori accuracy of the gradient model with the stability required in practical numerical simulations.