原始变量法计算封闭腔内自然对流

Calculations of the Natural Convection in an Enclosure with the Primitive Variables Numerical Method

在文献[1,2]的基础上,利用原始变量法求解封闭腔内自然对流换热问题.对求解域采用非等距交错网格剖分,利用泰勒级数于网格点展开取二阶精度进行(u,v,θ)方程各项的离散,采用SIMPLE方法对压力及压力修正进行求解.不同瑞利数(Ra)条件下的数值试验显示,该数值方法物理概念清晰,计算稳定.可通过调节网格的疏密等方法,达到改善求解的收敛及提高求解的精度等目的.

Based on the papers [1,2], the method for unsteady Navier-Stokes equations of primitive variables has been used for solving the natural convection flow and heat transfer in an enclosure. The field for solving is divided into non-equidistance and staggered grid analysis. The terms of the equations (u,v,θ) are discretized in some grid with Taylor's series with the second-order accuracy. The SIMPLE method is used for solving the pressure and the pressure revision. The simulations for various Rayleigh (Ra) numbers show that the numerical method is stable for calculations,and clear in the physics conceptions. The value B can be selected to adjust the grid's densities,so as to improve the convergence of the calculations and to raise the accuracy for solving the problems.