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In this paper, we demonstrate a set of fundamental conditions required forthe formulation of a thermohydrodynamic lattice Boltzmann model at an arbitraryPrandtl number. A specific collision operator form is then proposed that is incompliance 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 operatorform is theoretically shown to remove the well known non-Galilean invariantartifact at non-unity Prandtl numbers in previous thermal lattice Boltzmannmodels with multiple relaxation times.

Recovery of Galilean Invariance in Thermal Lattice Boltzmann Models for Arbitrary Prandtl Number