Double MRT Thermal Lattice Boltzmann Method for Simulating Natural   Convection of Low Prandtl Number Fluids
  The purposes of this paper are testing an efficiency algorithm based on LBM and using it to analyze two-dimensional natural convection with low Prandtl number. Steady state or oscillatory results are obtained using double multiple-relaxation-time thermal lattice Boltzmann method. The velocity and temperature fields are solved using D2Q9 and D2Q5 models, respectively. With different Rayleigh number, the tested natural convection can either achieve to steady state or oscillatory. With fixed Rayleigh number, lower Prandtl number leads to a weaker convection effect, longer oscillation period and higher oscillation amplitude for the cases reaching oscillatory solutions. At fixed Prandtl number, higher Rayleigh number leads to a more notable convection effect and longer oscillation period. Double multiple-relaxation-time thermal lattice Boltzmann method is applied to simulate the low Prandtl number fluid natural convection. Rayleigh number and Prandtl number effects are also investigated when the natural convection results oscillate. 
Zheng Li, Mo Yang and Yuwen Zhang
physics.comp-ph