(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
Natural convection in a square cavity at high Rayleigh numbers is simulated by multiple relaxation time (MRT) lattice Boltzmann method (LBM) with a separate distribution function to solve the temperature. The Rayleigh numbers examined here range from Ra=10^3 to Ra=10^8. For Rayleigh numbers below 10^8, the flow remains stationary and transition occurs beyond Ra=2×10^8. Unsteady results at higher Rayleigh numbers (Ra=10^9 and Ra=10^10) are also investigated. To the best of our knowledge, this is the first accurate study which involves the high Rayleigh numbers Ra=10^9, 10^10.