Thermal lattice Bhatnagar-Gross-Krook model for flows with viscous heat dissipation in the incompressible limit

Boltzmann Bhatnagar-Gross-Krook (BGK) equation for thermal flows with viscous heat dissipation in the incompressible limit was investigated. A temperature distribution function g was defined to represent the temperature field. The DDFLBGK model with two relaxation time can recover the correct macroscopic conservation equations for thermal flows with viscous heat dissipation in the incompressible limit and ensure that the EDF for each discrete velocity is non-negative. It was also suggested that the thermal lattice BGK model can also be applied in rather high Prandtl number flows and gives a reasonable accuracy.