As shown in the Figure 2-6, the PENTRAN results with S42 Legendre-Chebychev
quadratures are in good agreement with the MCNP5 results, and differences between the two are
within the statistical uncertainty of the Monte Carlo in air and the water phantom distal from the
source. Overall, this figure shows that increasing the angular quadrature order results in a
progressive improvement in solution accuracy, and that a substantial number of directions are
required for proper representation in air region between the source and the water phantom. We
further note that while the S12 leVel-Symmetric quadrature is quite adequate to represent neutron
scattering in nuclear engineering neutronics and reactor physics applications, it does not produce
accurate results here. For a general problem with a high degree of angular dependence, the ray-
effects must be largely mitigated by employing a large number of directions, i.e., a high-order
angular quadrature, From our analysis, a minimum of S32 Legendre-Chebychev quadratures
should be considered. Investigation of alternative, less computationally intensive methods for
mitigating the ray-effects in problems of this type has shown that ordinate biasing methodologies
can also be ofbenefitl9
1.OOE+10-
1.OOE+08-
-HSn22
Sn32
-MSn42
1.OOE+06 MMCNP5
1.OOE+04-
1.OOE+02-
1.OOE I O
O.OOE+OO 3.OOE+01 6.OOE+01 9.OOE+01
Distance (cm)
Figure 2-6. Scalar flux distributions using S12, S22, S32, and S42 with P3 Scattering anisotropy in
PENTRAN using the BUGLE-96 gamma library