Development of a coupled simplified lattice Boltzmann method for thermal flows

Abstract The simplified lattice Boltzmann method (SLBM) is relatively new in the LBM community, which lowers the cost in virtual memories significantly and has better numerical stability compared with the single-relaxation-time (SRT) LBM. Recently, SLBM has been extended to simulate thermal flows based on the simplified thermal energy distribution function model. However, the existing thermal models developed for SLBM are not strict in theory. In this work, a coupled simplified lattice Boltzmann method (CSLBM) for thermal flows and its boundary treatment are proposed, where the Navier-Stokes equations for the hydrodynamic field and the convection-diffusion equation for the temperature field are solved independently by two sets of SLBM equations. The consistent forcing scheme is adopted to couple the contribution of the temperature field to the hydrodynamic field. The boundary treatment for temperature field proposed in this work offers an analytical interpretation of the no-slip boundary condition. To validate the accuracy, efficiency, and stability of the present CSLBM, several canonical test cases, including the porous plate problem, the Rayleigh-Benard convection, and the natural convection in a square cavity are conducted. The numerical results agree well with the analytical solutions or numerical results in the literatures, which shows the present algorithm is of second-order accuracy in space and demonstrates the robustness of CSLBM in practical simulations.