Asymptotic derivation of the multigroup P-1 and simplified P-N equations with anisotropic scattering

The multigroup P1( )and simplified P-N (SPN) equations are derived by an asymptotic expansion of the multigroup transport equation with anisotropic scattering. The P-1 equations are the leading-order approximation in this expansion; the SPN equations for N = 2,3,... are increasingly higher order approximations. The physical assumptions underlying these approximations are that the material system is optically thick, the probability of absorption is small, and the mean scattering angle <(mu)over bar>(0) is not close to unity. For multigroup isotropic scattering transport problems, a dispersion analysis is given that verifies the accuracy of the SPN approximations. Numerical comparisons of P-1, SPN, and S-N solutions are also given. These comparisons show that for low N, SPN solutions are significantly more accurate (transportlike) than P-1 solutions and are obtained at a significantly lower computational cost than S-N solutions.