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

The PN 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 PN 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 PN equations agree with conventional formulations. However, at a boundary having a prescribed incident flux, the asymptotic boundary layer analysis yields PN boundary conditions that differ from previous formulations. Numerical transport and PN results are presented to substantiate this asymptotic theory.