A hybrid spatial differencing scheme for discrete ordinates method in 2D rectangular enclosures

A hybrid spatial differencing scheme for the discrete ordinates method is proposed to predict radiation intensity in a two-dimensional rectangular enclosure. Since the hybrid scheme incorporates the strengths from the diamond scheme and the step scheme, and takes into consideration the characteristics of the medium, it is more accurate and yields more stable results. Several other spatial differencing schemes are examined to address the effect of numerical smearing (or false scattering). Predictions from the present hybrid scheme are compared to those of the other schemes for transparent, purely absorbing, purely scattering, and absorbing–emitting–isotropically scattering media. It is found that the proposed scheme predicts more stable and less smeared results than the others.