Asymptotic derivation of the multigroup P[sub 1] and SP[sub N] equations
E.W. Larsen · Transactions of the American Nuclear Society · 1993
It has been known since the early 1970s that diffusion theory is an asymptotic limit of transport theory for one-group optically thick scattering-dominated transport problems. This asymptotic analysis has fostered a significant amount of research, such as the derivation of homogenization theories the analysis of numerical transport schemes for optically thick, diffusive systems, and the derivation of the simplified P[sub N] (SP[sub N]) equations. However, most of this previous analysis is applicable only to one-group transport problems. In this paper, we show that a related analysis can be used to derive asymptotically the multigroup P[sub 1], and multigroup SP[sub N] equations from the multigroup transport equation. As we have shown previously for one-group problems we show here that the multigroup SP[sub N] equations are higher order asymptotic corrections to the multigroup P[sub 1], equations. For simplicity, and because of space limitations, we only describe here the new asymptotic analysis for planar geometry and isotropic scattering. However, we have carried out the general analysis for the three-dimensional transport equation with anisotropic scattering and will publish a full description of this elsewhere.