Extension of a hybrid thermal LBE scheme for large-eddy simulations of turbulent convective flows

Following the work of Lallemand and Luo Lallemand P, Luo L-S. Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions. Phys Rev E 2003;68:036706] we validate, apply and extend the hybrid thermal lattice Boltzmann scheme (HTLBE) by a large-eddy approach to simulate turbulent convective flows. For the mass and momentum equations, a multiple-relaxation-time LBE scheme is used while the heat equation is solved numerically by a finite difference scheme. We extend the hybrid model by a Smagorinsky subgrid scale model for both the fluid flow and the heat flux. Validation studies are presented for laminar and turbulent natural convection in a cavity at various Rayleigh numbers up to 5 × 10¹⁰ for Pr = 0.71 using a serial code in 2D and a parallel code in 3D, respectively. Correlations of the Nusselt number are discussed and compared to benchmark data. As an application we simulated forced convection in a building with inner courtyard at Re = 50 000.