SIMULATION OF RAYLEIGH-BENARD CONVECTION USING A LATTICE BOLTZMANN METHOD

Rayleigh-Benard convection is numerically simulated in two and three d imensions using a recently developed two-component lattice Boltzmann e quation (LBE) method. The density field of the second component, which evolves according to the advection-diffusion equation of a passive sc alar, is used to simulate the temperature field. A body force proporti onal to the temperature is applied, and the system satisfies the Bouss inesq equation except for a slight compressibility. A no-slip, isother mal boundary condition is imposed in the vertical direction, and perio dic boundary conditions are used in horizontal directions. The critica l Rayleigh number for the onset of the Rayleigh-Benard convection agre es with the theoretical prediction. As the Rayleigh number is increase d higher, the steady two-dimensional convection rolls become unstable. The wavy instability and aperiodic motion observed, as well as the Nu sselt number as a function of the Rayleigh number, are in good agreeme nt with experimental observations and theoretical predictions. The LEE model is found to be efficient, accurate, and numerically stable for the simulation of fluid flows with heat and mass transfer.