On the propagation of rays in discrete ordinates

Discrete ordinates calculations are presumed to translate particles from ce ll to cell in the directions specified in the angular set. This should resu lt in uncollided particles from a small source propagating through the spat ial mesh in narrow beams in these directions. Accurate high-order angular q uadratures presume accurately attenuated propagation in the intended direct ions. This work examines the ability of various spatial quadratures to prop agate rays correctly. Some widely used methods are shown to fail at this fu damental task. Diamond-difference approximations introduce undamped lateral oscillations, resulting in severely unphysical flux representations. Nonli near fixups can prevent negativity but do not correct the underlying failur e to properly propagate pays. First-moment conserving schemes tend to be su ccessful but can be degraded in performance by simplifying approximations t hat are often used. Characteristic schemes are shown to have significant ad vantages. New characteristic methods are developed here that are exact (in a certain sense) in propagating rays and that uncouple the calculation of a djacent spatial cells in the mesh sweep. This enables DO loops to be conver ted to DO INDEPENDENT loops, with obvious implications for vector and/or pa rallel implementations.