Building a proper tensor-diffusivity model for large-eddy simulation of buoyancy-driven flows

Abstract

In this work, we plan to shed light on the following research question: can we ¿nd a nonlinear tensorial subgrid-scale (SGS) heat ¿ux model with good physical and numerical properties, such that we can obtain satisfactory predictions for buoyancy driven turbulent ¿ows? This is motivated by our recent ¿ndings showing that the classical (linear) eddy-di¿usivity assumption, qeddy ¿¿ T, fails to provide a reasonable approximation for the SGS heat ¿ux, q = uT - uT. This has been shown in our recent work [Dabbagh et al., Phys. Fluids 29, 105103 (2017)] where SGS features have been studied a priori for a Rayleigh-Bénard convection (RBC). We have also concluded that nonlinear (or tensorial) models can give good approximations of the actual SGS heat ¿ux. The nonlinear Leonard model, qnl ¿¿u¿T, is an example thereof. However, this model is unstable and therefore it cannot be used as standalone SGS heat ¿ux model. Apart from being numerically stable we also want to have the proper cubic near-wall behavior. Corrections in this regard will be presented together with a priori/posteriori studies of nonlinear SGS heat ¿ux models for RBC. Results from LES simulations will be compared with the DNS results obtained in the on-going PRACE project “Exploring new frontiers in Rayleigh-Bénard convection”.