Introduced a Modified Set of Boundary Condition of Lattice Boltzmann Method Based on Bennett Extension in Presence of Buoyancy Term Considering Variable Diffusion Coefficients

Various numerical boundary condition methods have been proposed to simulate various aspects of the no-slip wall condition using the Lattice Boltzmann Method. In this paper, a new boundary condition scheme is developed to model the no-slip wall condition in the presence of the body force term near the wall which is based on the Bennett extension. The error related to the new model is smaller than those of other boundary condition methods existing in the last studies. Based on the computational results, the body forces method which representing minimum error has been illustrated. Finally, the effect of the variation of diffusion coefficients on Rayleigh-Benard convection was studied. The critical Rayleigh number, which is obtained by current method, are in good agreement with the results calculated by the linear stability theory. It has been revealed that the proposed model is capable of computing the effect of high nonlinearity in the conservative equation in the presence of variable diffusion coefficients.