辐射热传导问题的SFVE格式与数值仿真

SFVE Schemes for Radiative Heat Conduction Problems in Cylindrical Coordinates and Numerical Simulations

在柱坐标系下,首先为多介质的输运管单温辐射热传导和多介质的三温辐射热传导两类模型问题,构造了一种针对非混合网格的保对称有限体元(SFVE-I)格式;接着针对一种特殊混合网格,分别为定常扩散和三温辐射热传导模型问题,构造了一种有限体元(FVE-II)格式;进行了数值实验与数值仿真,其结果表明:对定常问题,在一致网格上有限体元解函数关于真解函数和流函数的逼近分别具有二阶、一阶精度;对上述两种模型问题,数值仿真得到与实际物理现象基本相符的热传导过程和温度分布,且能量守恒误差均小于5%。

Firstly,SFVE scheme was given on the non-mixed grid for two kinds of the radiative heat conduction equations,and FVE scheme was provided on the special mixed grid for the stationary diffusion problem and the radiative heat conduction equations.Numerical experimental and simulative results show that the new schemes have smaller energy conservation error（less than 5%） and hold saturated convergent order approximating to the exact solution and flux function for the stationary diffusion problem on the uniform mesh.Numerical simulation results of heat conduction are consistent with the actual physical phenomenons.