THE PN THEORY AS AN ASYMPTOTIC LIMIT OF TRANSPORT-THEORY IN PLANAR GEOMETRY .2. NUMERICAL RESULTS

The P(N) theory has been shown to be an asymptotic limit of transport theory for problems in optically thick planar-geometry media with low absorption rates and highly anisotropic scattering. Transport problems that lie outside the asymptotic regime of validity of P(N) theory are considered. Such problems occur in media that are either optically thin, or contain isotropic or mildly anisotropic scattering, or are not weakly absorbing. For such problems, the accuracy of numerical solutions of the P(N) equations obtained using the asymptotic boundary conditions is demonstrated. These numerical solutions are compared with others obtained using various familiar boundary conditions. Solutions obtained using the asymptotic boundary conditions are always competitive with, and often superior to, solutions obtained using these other boundary conditions.