A New Multiple-relaxation-time Lattice Boltzmann Method for Natural Convection

This article is devoted to the study of multiple-relaxation-time (MRT) lattice Boltzmann method with eight-by-eight collision matrix for natural convection flow. In the velocity space, eight speed directions are used and the corresponding incompressible multiple-relaxation-time model with force term is presented. D2Q4 model is for temperature field. The coupled double distribution functions (DDF) overcome artificial compressible effect corresponding to the standard MRT model. The simulations of natural convection flows with Pr=0.71 for air and Ra=10(3)-10(9) are carried out and excellent agreements are obtained to demonstrate the numerical accuracy and stability of the proposed model.