【摘要】 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。采用常规的有限元法求解这个对流占优问题,解往往会出现非物理振荡。为消除解的非物理振荡,该文发展了基于流线迎风(SU)格式及彼得罗夫–迦辽金流线(SUPG)格式的有限元法来求解半透明介质的多维辐射传输问题,并对2种迎风格式求解辐射传递方程的性能进行了比较。结果表明,2种迎风格式都起到了很好的稳定作用,均能有效消除解的非物理振荡,从求解精度上来看,SUPG格式要优于SU格式。采用2个算例对提出的方法进行验证,与文献中得到的无量纲温度及净辐射热流分布较,结果表明提出的迎风有限元方法对于求解多维半透明介比质内的辐射传递有着很好的精度。更多还原

【Abstract】 Radiative transfer equation (RTE) in cartesian coordinates can be considered as a special kind of convective- diffusive equation with strong convection characteristics. For this convection dominated problem, standard finite element solutions often suffer from spurious oscillations. To avoid this, upwind finite element methods based on streamline upwinding (SU) and streamline upwinding petrov-galerkin (SUPG) schemes are developed to solve multidimensional radiative heat transfer in semitransparent media. Comparison between these two upwind schemes on the solution of RTE is carried out. It is shown that the SUPG scheme is better than the SU scheme as far as solution accuracy is concerned. Two test cases are taken as examples to verify the presented methods. The distributions of dimensionless temperature and net wall heat flux are calculated and compared to the results in references. By comparison, it is shown that the upwinding finite element methods developed have good accuracy in solution of radiative heat transfer in semitransparent media.更多还原