Recovery of Galilean Invariance in Thermal Lattice Boltzmann Models for   Arbitrary Prandtl Number
  In this paper, we demonstrate a set of fundamental conditions required for the formulation of a thermohydrodynamic lattice Boltzmann model at an arbitrary Prandtl number. A specific collision operator form is then proposed that is in compliance with these conditions. It admits two independent relaxation times, one for viscosity and another for thermal conductivity. But more importantly, the resulting thermohydrodynamic equations based on such a collision operator form is theoretically shown to remove the well known non-Galilean invariant artifact at non-unity Prandtl numbers in previous thermal lattice Boltzmann models with multiple relaxation times. 
Hudong Chen, Pradeep Gopalakrishnan and Raoyang Zhang
physics.flu-dyn nlin.CG physics.comp-ph