Implementation of diffuse reflection boundary conditions in a thermal lattice Boltzmann model with flux limiters

We discuss three new implementation versions of diffuse reflection boundary conditions in a thermal lattice Boltzmann model. Their accuracy is investigated in the case of Couette flow by considering the slip regime. The best results are recovered with versions 2 and 3, which rely on outgoing fluxes to express the particle distribution functions in the ghost nodes outside the flow domain. Version 2 is found to be more economical since it involves no interpolation procedure. This version was thereafter used to investigate the temperature profile in Couette flow for various values of Prandtl number, as well as the capability of the thermal LB model to capture the Knudsen minimum in Poiseuille flow.