Effects of S_N Method Numerics on Pressure Vessel Neutron Fluence Calculations

An accurate prediction of the reactor pressure vessel (PV) fast neutron fluence (E> 1.0 MeV or E> 0.1 MeV) is necessary to ensure PV integrity over the design lifetime. The discrete ordinates method (S_N method) is the method of choice to treat such problems, and the DORT S_N code is widely used as a standard tool for PV fluence calculations. The S_N numerics and the corresponding DORT numerical options and features offer alternative choices that increase flexibility but also impact results. The effects of S_N numerics based on PV fluence calculations for two pressurized water reactors are examined. The differencing schemes [linear, zero-weighted (ZW), and θ-weighted (TW)] and their interactions with spatial and angular discretization are also examined. The linear and TW ( θ = 0.9) schemes introduce unphysical flux oscillations that for certain groups and positions may exceed 10%. The ZW scheme produces smooth results; however, its results differ from the other two schemes. A good compromise for PV fluence calculations is a TW scheme with a small θ value (i.e., θ = 0.3), which reduces the uncertainty to ∼3%. Angular discretization and spatial mesh size employed in typical calculations introduce another ∼3 and ∼2% uncertainty, respectively. The analysis further shows that the fixup is not necessary for the negative scattering source. The pointwise convergence criterion is also not a critical issue in the fast energy range because of a relatively fast convergence rate. Similarly, acceleration parameters impact mainly the execution time and only marginally the results. The root-mean-square combined uncertainty for standard PV fluence calculations due to the options analyzed is ∼5%.