Multiple Relaxation Time Lattice Boltzmann Simulation of 2D Natural Convection in a Square Cavity at High Rayleigh Numbers

Abstract

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 $Ra=10^9$, $10^{10}$.