方腔内自然对流与混合对流的有限差分格子Boltzmann研究

A Finite-Difference Lattice Boltzmann Method for the Simulation of Natural and Mixed Convection Flows in a Square Cavity

基于有限差分法,建立了贴体坐标系下求解流体流动和传热的双分布格子Boltzmann模型.在密度分布函数和温度分布函数对应的离散速度方程中,时间项采用四阶Runge-Kutta法离散,空间离散采用二阶迎风和二阶中心差分的混合形式.采用此模型分别对瑞利数为10^3、10^4、10^5、10^6的方腔自然对流以及理查森数为0.1、1、10的方腔混合对流进行了数值模拟,获得了流体速度与温度分布的典型特征,得到的努塞尔数也与基准解高度吻合.计算结果表明了本文采用的数值方法和计算程序的有效性.

The implementation of a finite-difference lattice Boltzmann method based on double-population approach for body-fitted coordinates was performed. For both velocity and temperature fields, the spatial derivatives discretized by combining the upwind scheme with the central scheme and the temporal term was discretized with fourth-order Runge-Kutta scheme. Natural convection and mixed convection flows in a two-dimensional square cavity were simulated numerically. Studies were carried out for natural convection flows as Rayleigh numbers range from 1.0×10~3 to 1.0×10~6 as well as mixed convection flows as Richardson numbers range from 0.1 to 10. Results were presented in terms of streamlines, isotherms and Nusselt numbers. Excellent agreement is obtained between our results and benchmark solution. The different comparisons demonstrate the accuracy of our proposed approach.