Discrete ordinates methods for radiation transport

The discrete ordinates (SN) method, first developed for stellar atmospheres, has been used extensively on various other radiation transport problems. In reactor analysis the method is generally used to generate parameters for design models based on more approximate but less expensive methods (such as diffusion theory) so that the spatial-spectrum coupling is represented accurately on a microscopic reaction rate level. It has a decisive advantage over Monte Carlo methods in computing the pin and assembly power profiles. In shielding problems where the penetration of the radiation can be deep, the method is used widely in design calculations. In oil-well logging problems, which also involve deep penetration and have a stringent accuracy requirement on the detector responses, the method complements the Monte Carlo techniques. One early application of the SN method was on one-dimensional radiative transfer problems. The discrete ordinates method has also been used in charged-particle transport problems. While the method has been applied primarily to static problems, one-dimensional time-dependent codes have existed since the early 1970s. In this paper the authors briefly review the basic method, illustrate its applications, discuss its merits and pitfalls, and enumerate the recent advances in the attendant numerical techniques that have enhanced the capabilities of the method