Spatial Differencing Schemes of the Discrete-Ordinates Method

Several spatial differencing schemes are used to discretize the radiative transfer equation in the context of the discrete-ordinates method. These are the conventional upwind, central, hybrid, and exponential schemes as well as the high-resolution SMART scheme. The deferred correction strategy is adopted to incorporate the SMART scheme into the discrete-ordinates method. The TN quadrature set is used. Two nonscattering benchmark problems in two and three dimensions and one three-dimensional anisotropically scattering problem are considered. The radiation intensity is sensitive to the spatial differencing scheme used, while integral quantities are somewhat insensitive to the spatial differencing scheme. The SMART scheme yields accurate, nonoscillatory, and positive radiation intensity distributions. The central, exponential, and SMART schemes are almost equally accurate in the prediction of radiative heat transfer in both nonscattering and scattering media.