基于热格子Boltzmann方法的自然对流数值模拟

SIMULATION OF NATURAL CONVECTION FLOW BY THE THERMAL LATTICE BOLTZMANN METHOD

对Eggels和Somers提出的热格子Boltzmann格式进行了改进.在不可压缩流动的假设下,提出了一种新的温度平衡分布函数,可以克服压缩性对温度统计的影响,并且相应地修正了统计宏观温度的方法.Eggels和Somers的方法对速度和温度均采用半步长反弹格式边界条件,适合无滑移的速度边界条件.但是对温度采用该边界条件在物理本质上显得不够准确,所以在边界上对二者统一采取算法既简单又容易实现的非平衡态外推格式,同时可以与Boltzmann格式的整体二阶精度保持一致.最后,利用改进的热格子Boltzmann方法（TLBM）模拟了Ra=10^6和Pr=0.71（空气）的方腔中的自然对流,模拟得到的流动参数与其它数值方法的结果吻合得很好,表明改进的热格子Boltzmann方法可以有效准确地模拟非等温流动.

In this paper, the thermal lattice Boltzmann scheme has been improved, which was proposed by J. G. M. Eggels and J. A. Somers, and a new equilibrium solution for temperature distribution function has been presented on the incompressible flow assumption. This new equilibrium solution can correct the compressibility effect on macroscopic temperature, and modify the statistical definition of macroscopic temperature. The half-way bounce-back boundary condition was used in the method proposed by J. G. M. Eggels and J. A. Somers for velocity and temperature. However, the boundary condition was not accurate for the temperature in the physical view. Therefore, a non-equilibrium extrapolation scheme, which is a simple algorithm and very easy to implement, has been adopted for velocity and temperature in the boundaries. Subsequently, the improved TLBM has been used to simulate the natural convection in the cavity at Ra = 106 and Pr = 0.71 for air. The flow parameters obtained in the simulation agreed very well with those of other numerical methods, to indicate that the improved TLBM can be used to simulate the non-isothermal flows efficiently and accurately.