A simple lattice Boltzmann model for turbulence Rayleigh-Bénard thermal convection

A simple lattice Boltzmann thermal model is proposed for simulating the turbulence Rayleigh-Bénard convection. This new model introduces a mesoscopic external force term in the lattice Boltzmann equation to consider the effect of the buoyant body force and introduces a temperature density distribution function to simulate the temperature field. The macroscopic density and velocity fields are simulated using the density distribution function. The results show that this simple model is able to simulate turbulence Rayleigh-Bénard convection in the current simulation range of 106⩽Ra⩽1012. It is shown that the energy spectra of the velocity and temperature are in good agreement with the Bolgiano-Obukhov-like (BO59) scaling.