Abstract
In the present paper, we verify the effectiveness of the two-relaxation-time (TRT) collision operator in reducing boundary slip of temperature computed by the immersed boundary-thermal lattice Boltzmann method (IB-TLBM). In the linear collision operator of the TRT, we decompose the distribution function into symmetric and antisymmetric components and define the relaxation parameters for each part. The Chapman-Enskog expansion indicates that one relaxation time for the antisymmetric component is related to the thermal conductivity. We derive the theoretical relation between a temperature slip at the boundary and reveal that the relaxation time for the symmetric part controls the temperature at the boundary and boundary slip of temperature computed by the IB-TLBM. We apply the IB-TLBM based on the implicit correction method with two relaxation times for the natural convection in a square enclosure containing a circular cylinder. The streamline, isotherms, and average Nusselt number calculated by the proposed method agree well with those of previous numerical studies.
