  Multiple-relaxation-time model (MRT) has more advantages than the many others
approaches in the Lattice Boltzmann Method (LBM). Three-dimensional double MRT
model is proposed for the first time for fluid flow and heat transfer
simulation. Three types of cubic natural convection problems are solved with
proposed method at various Rayleigh numbers. Two opposite vertical walls on the
left and right are kept at different temperatures for all three types, while
the remained four walls are either adiabatic or have linear temperature
variations. For the first two types of cubic natural convections that four
walls are either adiabatic or vary linearly, the present results agreed very
well with the benchmark solutions or experimental results in the literature.
For the third type of cubic natural convection, the front and back surfaces has
linearly variable temperature while the bottom and top surface are adiabatic.
The results from the third type exhibited more general three-dimensional
characters.
