On a Proper Tensor-Diffusivity Model for Large-Eddy Simulations of Buoyancy-Driven Flows

Abstract

In this work, we plan to shed light on the following research question: can we find a nonlinear subgrid-scale (SGS) heat flux model with good physical and numerical properties, such that we can obtain satisfactory predictions for buoyancy-driven turbulent flows? This is motivated by our findings showing that the classical (linear) eddy-diffusivity assumption fails to provide a reasonable approximation for the SGS heat flux. This was shown in our work [1] where SGS features have been studied a priori for a Rayleigh–Bénard convection (RBC). We also concluded that nonlinear (or tensorial) models can give good approximations of the actual SGS heat flux. Briefly, the large-eddy simulation (LES) equations arise from applying a spatial commutative filter, with filter length δ, to the incompressible Navier–Stokes and thermal energy equations.