Recent developments in the solution of radiation heat transfer using the discrete ordinates method

This paper focuses on some of the shortcomings of the discrete ordinates method. Some are crucial to the solution accuracy, while others affect the efficiency of the solution procedure. The shortcomings reviewed in this paper are the ray effect, excessively long computational times in optically thick media, effects of spatial differencing schemes, and false scattering. A recent proposal for a more efficient treatment of the in-scattering term, that reduces the computational times for optically thick scattering media, is described. A study of several spatial differencing schemes, that showed that the diamond scheme can produce physically unrealistic solutions for some multidimensional computations, is discussed. Recommendations for a better differencing scheme that would also reduce false scattering are given.