investigation on instability of rayleighbenard convection using lattice boltzmann method with a modified boundary condition

In this study, the effects of prandtl number on the primary and secondary instability of the rayleigh-benard convection problem has been investigated using the lattice boltzmann method. two different cases as pr=5.8 and 0.7 representing the fluid in liquid and gas conditions are examined. a body forces scheme of the lattice boltzmann method was presented. two types of boundary conditions in the presence of body forces are analyzed by the moment method and applied to a poiseuille flow. characteristic velocity was set in such a way that the compressibility effects are negligible. the calculations show that the increment of prandtl number from 0.7 to 5.8 causes to create a secondary instability and onset of the oscillation in the flow field. results show that at pr=5.8, when the rayleigh number is increased, a periodic solution appeared at ra=48,000. it is observed that the dimensionless frequency ratio for ra= 10^5 with pr=5.8 is around 0.0065. the maximum nusselt number for ra = 10^5 with pr=5.8 are estimated to be 5.4942.