Parallel Pentran Solutions of the “tiel” Steady State Neutron Transport Benchmark Problems

The TIEL benchmarks include a set of analytical benchmark solutions to the transport equation in infinite media. In this paper, we present solutions for the infinite planar, point, spherical shell, and solid spherical sources solved using the PENTRAN 3-D Parallel SN code compared to reference solutions of the TIEL benchmark problems. Excellent agreement (less than 0.7% difference) was achieved when comparing reference solutions with PENTRAN scalar fluxes in the case of planar, shell and solid sphere sources. Depending on the scattering properties and the geometry of the system, Legendre-Chebychev quadratures as high as S34 for the planar or S54 for the spherical symmetry sources, with appropriate spatial discretization, were needed to properly represent the flux. Inherent numerical difficulties were encountered when finding the solution in the very close proximity (< 0.1 mfp) of the sources.