ThePNTheory as an Asymptotic Limit of Transport Theory in Planar Geometry —I: Analysis

Abstract

In this paper the P{sub N} theory is shown to be an asymptotic limit of transport theory for an optically thick planar-geometry system with small absorption and highly anisotropic scattering. The asymptotic analysis shows that the solution in the interior of the system is described by the standard P{sub N} equations for which initial, boundary, and interface conditions are determined by asymptotic initial, boundary layer, and interface layer calculations. The asymptotic initial, (reflecting) boundary, and interface conditions for the P{sub N} equations agree with conventional formulations. However, at a boundary having a prescribed incident flux, the asymptotic boundary layer analysis yields P{sub N} boundary conditions that differ from previous formulations. Numerical transport and P{sub N} results are presented to substantiate this asymptotic theory.