A simple difference method for lattice Boltzmann algorithm to simulate conjugate heat transfer

•The present method is simple and easy to implement, it just need to correct the streaming process.•The difference method can deal with curved interface easily with staircase approximation.•It exhibits good stability against large ranges of thermal conductivity ratio ks/kf and heat capacity ratio (ρcp)s/(ρcp)f. In the present paper, a simple difference method for lattice Boltzmann algorithm is proposed to simulate conjugate heat transfer problems. In the conventional lattice Boltzmann method (LBM), the informations including temperature and heat flux exchange directly between two different media through distribution function during the streaming process, however, the continuity of heat flux at the interface between two different media cannot be guaranteed in this process. Different with the conventional LBM, we consider that the nodes near the interface get the distribution functions from the interface during the streaming process across the interface. The distribution functions at the interface can be obtained by coupling the interface conditions of temperature and heat flux with non-equilibrium extrapolation. Four test cases are used to validate the present method, including both steady and transient conjugate heat transfer with flat or curved interfaces. The results show that the present method is very easy to implement, and feasible for both steady and transient heat transfer problems. In addition, for simplicity, by approximating the real interface with a staircase shaped line, the present method can deal with curved interface easily and the results show the approximation will not contribute obvious error to the final results.