2.6 Discussions and Findings
In this chapter, we highlighted recent studies examining the discretization requirements
of the deterministic SN method compared with the Monte Carlo method with application to
dosimetry problems. In doing so, we chose to simulate an idealized 3-D 60C0 model using the
PENTRAN code. Since radiation transporting in such applications encounters little interaction in
low density materials, such as air, attention was given to the quadrature level and mesh size
distribution needed for solution accuracy through the air and in a water phantom. As expected,
radiation transport in this gamma ray application is highly directional, and that a traditional SN
quadrature, such as an S12 leVel-Symmetric set (168 total directions), considered robust for many
neutron reactor physics applications, is insufficient for modeling gamma rays in the 60C0 model.
This limitation was overcome by the use of the higher levels of quadrature, up to S42 (1848 total
directions per cell) with Legendre-Chebychev quadrature sets and P3 anisotropy. We also noted
that at least an S32 angular quadrature leads to the elimination of most ray effects and scalar
fluxes within the statistical uncertainty of Monte Carlo. Moreover, model mesh sizes were
selected to preserve system volumes while taking into account the optical thickness of each
material. Smaller Cartesian meshes do better represent the curvature of the model, but they
require higher quadrature orders, and therefore larger memory and longer running times. Even in
optically thin air regions, a mesh cell interval of on the order of 1 cm was necessary to yield an
accurate solution, and more cells were necessary where the particle flux encountered strong
gradients; cell intervals may be relaxed near boundaries where detail is not required. Also of
importance was the flexibility of the ADS in PENTRAN, permitting more appropriate spatial
differencing schemes. Scalar flux distributions obtained from PENTRAN agreed with the Monte
Carlo prediction when simulating equivalent geometry models of the 60C0 model with three
different multigroup cross-section libraries. Still, realistic representations of the energy spectra