中文摘要：

推导多维梯度折射率介质内稳态辐射传递的扩散近似方程.使用有限元法对扩散近似进行离散和求解,利用两个二维半透明介质的稳态辐射传递问题验证该扩散近似的精度及适用性.算例考虑介质为均匀折射率及梯度折射率两种情况.利用扩散近似分别求解辐射平衡时的边界热流、介质内温度场分布,并与辐射传递方程的求解结果进行对比分析.结果表明：介质折射率变化、散射特性、光学厚度及散射反照率均直接影响扩散近似的精度;在光学厚及强散射条件下,该扩散近似可以作为一种快速算法应用于梯度折射率介质稳态辐射传递的求解.

英文摘要：

A diffusion approximation equation was derived for steady radiative transport in graded index media. With discretization and finite element method, steady radiative heat transfer in two-dimensional rectangular gray semitransparent medium are examined to verify performance of the diffusion approximation. Cases with uniform index distribution and graded index distributions are considered. Boundary radiative heat flux and media temperature distribution under radiative equilibrium are determined with diffusion approximation and compared with results of radiative transfer equation. It shows that accuracy of the diffusion approximation is influenced by index, scattering characteristics,optical depth and scattering albedo. As the medium is optical thick and scattering is strong, the diffusion approximation shows good accuracy and can be considered as a rapid algorithm for steady radiative transfer problem in a semitransparent graded index medium.