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

Abstract

In this paper, by introducing a different distribution function and starting from the Boltzmann equation as well as the Maxwell-Boltzmann distribution, we obtain a Boltzmann Bhatnagar-Gross-Krook (BGK) equation for thermal flows with viscous heat dissipation in the incompressible limit. The continuous thermal BGK model is then discretized over both time and phase space to form a lattice BGK model, which is shown to be consistent with some existing double distribution function lattice BGK models based on macroscopic governing equations. We have also demonstrated that the lattice BGK model derived theoretically in this work can be used to simulate laminar incompressible convention heat transfer with/without viscous heat dissipation.