Diffusion Asymptotics With Fully Anisotropic Source and Scattering

Abstract

Here we investigate the asymptotic diffusion limit on the interior of a transport domain for the case of steady-state 1-D slab geometry with fully anisotropic scattering and distributed sources. By this we mean that the scattering and distributed sources are described by a Legendre expansion of infinite degree. It is found that the asymptotic equation for the scalar flux obtained through first order is identical to that obtained with P₁ scattering and distributed sources. However, the leading-order equation differs from that obtained via the traditional Galerkin method assuming a P₁ angular flux dependence and P₁ scattering and distributed source expansions. In particular, the first moment of the distributed source does not appear in the leading-order equation for the scalar flux as it does in the Galerkin equations for the scalar flux.

Keywords:

• asymptotic diffusion limit

Disclosure statement

No potential conflict of interest was reported by the author.