The calculation method for SP3 discontinuity factor and its application

Abstract The simplified-P3 (SP 3 ) method is considered a promising approximate spherical harmonics method with comparable accuracy to low order discrete ordinate method, but with about the same order of speed as that of the diffusion method. However the difficulty in calculating the SP 3 discontinuity factors (DF) could significantly reduce its advantage over the diffusion method for practical applications. Recently Chao and Yamamoto proposed a new SP 3 derivation that overcomes this difficulty with the explicit derivation of how to calculate DF in terms of the volume average flux, surface average flux, surface average partial currents, and the surface average flux gradient from the heterogeneous transport solution of a single reflective assembly. This paper follows that formulation and approach, but with an error correction and some improvements, to work out a specific methodology of calculating DF for SP 3 and validates the method with a set of challenging numerical benchmark problems. It is concluded that although SP 3 is significantly more accurate than diffusion, diffusion with DF actually gives more accurate results than SP 3 without DF. However, when SP 3 also uses DF its superiority over diffusion is restored. But in case of energy group collapsing or large nodal meshes, the advantage of using SP 3 over diffusion diminishes.