LES-based filter-matrix lattice Boltzmann model for simulating turbulent natural convection in a square cavity

In this paper, a novel thermal filter-matrix lattice Boltzmann model based on large eddy simulation (LES) is proposed for simulating turbulent natural convection. In this study, the Vreman subgrid-scale eddy-viscosity model is introduced into the present framework of LES to accurately predict the flow in near-wall region. Two dimensional numerical simulations of natural convection in a square cavity were performed at high Rayleigh number varying from 10⁷ to 10¹⁰ with a fixed Prandtl number of Pr=0.71. The influences of the higher-order terms upon the present results at high Rayleigh numbers are examined, taking Ra=10⁷ and 10⁸ as the example, revealing that the proper minimization of the higher-order terms can improve numerical accuracy of present model for high Rayleigh convective flow. For the turbulent convective flow, the time-averaged quantities in the median lines are presented and compared against those available results from previous studies. The general structure of turbulent boundary layers is well predicted. All numerical results exhibit good agreement with the benchmark solutions available in the previous literatures.