Numerical implementation of thermal boundary conditions in the lattice Boltzmann method

This work proposed a non-equilibrium mirror-reflection scheme to implement thermal boundary conditions for the two-distribution lattice Boltzmann method (TLBM). The study showed that the most popular non-equilibrium bounce-back scheme would become inadequate when the predictions of temperature gradient were examined in TLBM. This work used the native method in TLBM to verify temperature gradient instead of the conventional finite difference approximation. The simulation results demonstrated that the mirror-reflection scheme is a scheme of second-order accuracy and can predict the temperature and temperature gradient correctly. With help of calculating the heat flux on the boundary, this work also suggested a more efficient and realistic way to determine the Nusselt number in Rayleigh–Bénard convection problems.