求解多维半透明介质内辐射传递的谱元法

直角坐标系下的辐射传递方程可以看作一类特殊的对流扩散方程，且具有强对流特性。采用数值方法求解该问题需要特别的稳定技术，否则计算结果往往会出现非物理振荡现象。本文发展了基于流向迎风彼得罗夫-伽辽金（SUPG）格式的谱元法来求解多维半透明介质内的辐射传递。采用3个算例对SUPG谱元法求解多维半透明介质内辐射传递的性能进行了检验。结果表明，与伽辽金谱元法相比，SUPG谱元法有效地消除了解的非物理振荡现象，同时与解析解及文献中的结果相比较，SUPG谱元法对于求解多维半透明介质内的辐射传递有着很好的精度。

Spectral element method for solving radiative heat transfer in semi-transparent media

Radiative transfer equation(RTE)in Cartesian coordinates can be considered as a special kind of convective-diffusive equation and is convection dominated.Numerical solution of the convection dominated problem often suffers from spurious oscillations.The spectral element method based on streamline upwind Petrov-Galerkin(SUPG)stabilization scheme was developed to solve multidimensional radiative heat transfer in semi-transparent media.Three test cases were taken as examples to verify the performance of the SUPG spectral element method for solving multi-dimensional radiative heat transfer in semi-transparent media.The SUPG spectral element method effectively diminished the spurious oscillations as compared with the Galerkin spectral element method.The distributions of radiative intensity and net wall heat flux were calculated and compared with the analytical results and data in references.By comparison,it was shown that the SUPG spectral element method developed in this paper had good accuracy in solving radiative heat transfer in semi-transparent media.