The Simplified-$DP_N$ Approximation of the Neutron Transport Equation

Abstract

The simplified double-spherical harmonics ($SDP_N$) approximation of the neutron transport equation is proposed. The $SDP_N$ equations are derived from the multi-group $DP_N$ equations for N=1,2,3 (equivalent to the $SP_3$, $SP_5$, and $SP_7$ equations, respectively), and are converted into the form of second order multi-group diffusion equations. The finite element method is then used to numerically solve these equations. The computational performance of the $SDP_N$ method is compared with the $SP_N$ on several fixed-source and criticality test problems. The results show that the $SDP_N$ formulation generally calculates parameters like criticality eigenvalue, disadvantage factors, absorption rate, etc. more accurately than the $SP_N$, while the computational effort is the same for both methods.Comment: 20 pages, 9 figures, 11 table