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-Bénard 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.

简化格子玻尔兹曼方法 (SLBM) 在 LBM 社区中相对较新，与单松弛时间 (SRT) LBM 相比，它显着降低了虚拟存储器的成本并具有更好的数值稳定性。最近，SLBM 已经扩展到基于简化的热能分布函数模型来模拟热流。然而，现有的 SLBM 热模型在理论上并不严格。在这项工作中，提出了一种用于热流及其边界处理的耦合简化晶格玻尔兹曼方法 (CSLBM)，其中流体动力场的纳维-斯托克斯方程和温度场的对流-扩散方程通过两组独立求解SLBM 方程。采用一致强迫方案来耦合温度场对水动力场的贡献。这项工作中提出的温度场边界处理提供了无滑移边界条件的解析解释。为了验证当前 CSLBM 的准确性、效率和稳定性，进行了几个典型的测试案例，包括多孔板问题、Rayleigh-Bénard 对流和方腔中的自然对流。数值结果与文献中的解析解或数值结果吻合较好，表明该算法在空间上具有二阶精度，证明了CSLBM在实际模拟中的鲁棒性。这项工作中提出的温度场边界处理提供了无滑移边界条件的解析解释。为了验证当前 CSLBM 的准确性、效率和稳定性，进行了几个典型的测试案例，包括多孔板问题、Rayleigh-Bénard 对流和方腔中的自然对流。数值结果与文献中的解析解或数值结果吻合较好，表明该算法在空间上具有二阶精度，证明了CSLBM在实际模拟中的鲁棒性。这项工作中提出的温度场边界处理提供了无滑移边界条件的解析解释。为了验证当前 CSLBM 的准确性、效率和稳定性，进行了几个典型的测试案例，包括多孔板问题、Rayleigh-Bénard 对流和方腔中的自然对流。数值结果与文献中的解析解或数值结果吻合较好，表明该算法在空间上具有二阶精度，证明了CSLBM在实际模拟中的鲁棒性。并在方腔内进行自然对流。数值结果与文献中的解析解或数值结果吻合较好，表明该算法在空间上具有二阶精度，证明了CSLBM在实际模拟中的鲁棒性。并在方腔内进行自然对流。数值结果与文献中的解析解或数值结果吻合较好，表明该算法在空间上具有二阶精度，证明了CSLBM在实际模拟中的鲁棒性。