Simulating oscillatory flows in Rayleigh–Bénard convection using the lattice Boltzmann method

Rayleigh–Bénard convection is a fundamental phenomenon found in many atmospheric and industrial applications. Many numerical methods have been applied to analyze this problem, including the lattice Boltzmann method (LBM), which has emerged as one of the most powerful computational fluid dynamics (CFD) methods in recent years. Using a simple LB model with the Boussinesq approximation, this study investigates the 2D Rayleigh–Bénard problem from the threshold of the primary instability with a theoretical value of critical Rayleigh number Ra c = 1707.76 to the regime near the flow bifurcation to the secondary instability. Since the fluid of LBM is compressible, an appropriate velocity scale for natural convection, i.e. V ≡ β g y Δ TH , is carefully chosen at each value of the Prandtl number to ensure that the simulations satisfy the incompressible condition. The simulation results show that periodic unsteady flows take place at certain Prandtl numbers with an appropriate Rayleigh number. Furthermore, the Nusselt number is found to be relatively insensitive to the Prandtl number in the current simulation ranges of 0.71 ⩽ Pr ⩽ 70 and Ra ⩽ 10 5 . Finally, the relationship between the Nusselt number and the Rayleigh number is also investigated.