Anisotropic Eigenvalue Spectrum Calculations of the Neutron Transport Operator with Low-Order Spatial Expansion Methods

The results of a numerical analysis of the eigenvalue spectrum and eigenmodes of the monoenergetic integral transport equation are presented. Anisotropic scattering effects are explicitly considered with P₁ and P₂ expansions. Benchmark quality data are produced for three related onedimensional homogeneous multiplying slab problems: fuel with vacuum boundary, fuel with reflectors, and fuel/reflector infinite lattice. Two low-order spatial expansion techniques are investigated and shown to be equivalent in accuracy to analytical or high-order spatial expansion methods. The weak finite element formulation is shown to be slightly more accurate than the comparably sized quadrature formulation. The calculational results of the isotropic and anisotropic analysis are compared with data available in the literature and extended to provide additional results reflecting the effects of linearly and quadratically anisotropic scattering.