Anisotropic Scattering Approximations in the Monoenergetic Boltzmann Equation

The effects of anisotropic scattering approximations in the monoenergetic transport equation are evaluated by calculating discrete eigenvalues, fluxes due to a plane source, and slab critical half-thicknesses, all for homogeneous media. Relative to P₂ scattering approximation results, which are deemed accurate because of their agreement with P₄ solutions, the simple transport approximation overestimates eigenvalues and underestimates half-thicknesses in multiplying media while a P₁ scattering approximation underestimates eigenvalues and overestimates thicknesses, but with smaller error. In the plane source problem, where the detailed flux behavior is observed, the transport approximation is even less accurate; but an extended transport approximation is found to be much more adequate. In overall effectiveness, in order of increasing accuracy, the approximations considered are ranked as follows: 1) transport, 2) forward-backward, 3) first-order Legendre, 4) extended transport, and 5) higher order Legendre. Some evidence is given to indicate that, even for severely anisotropic scattering, relatively low-order Legendre approximations are sufficient to include anisotropic scattering effects.