On the possible gain of the application of the sp3 solution in nodal codes

The simplified PN method has attracted much attention in reactor physics. The implementation of an increased order expansion has the potential to improve the results. It is investigated if this potential can be released under the specific features of nodal codes with fuel assembly sized calculation cells.
One dimensional analytical solutions for the one and two energy-group diffusion, SP3 and P3 equations are derived. The results are compared with reference solutions calculated with ONEDANT and HELIOS. Tests are performed on the Brantley, Larsen one-group test case and on a pin cell with real reactor materials. For the evaluation of the differences between the diffusion and the SP3 solutions in the nodal code configuration, benchmark configurations are investigated.
A comparison of the diffusion and the SP3 results show improvements for the test case using fuel element size nodes when compared to a reference solution using the identical cross section basis. Comparing with a multi-group reference solution shows that the diffusion solution sometimes behaves better due to error cancellation. To achieve the full gain of the SP3 method in nodal calculations, a new standard for light water reactor calculations has to be defined with a refined energy-group structure.