Simplified-DPN treatment of the neutron transport equation

TL;DR

This paper introduces the simplified double-spherical harmonics (SDPN) method for neutron transport equations, converting them into diffusion equations and demonstrating improved accuracy over traditional SPN methods with similar computational effort.

Contribution

The paper develops the SDPN approximation from multi-group DPN equations and shows it achieves higher accuracy than SPN methods without increased computational cost.

Findings

SDPN provides more accurate criticality eigenvalues.

SDPN outperforms SPN in absorption rate calculations.

Computational effort remains comparable to SPN methods.

Abstract

In this paper the simplified double-spherical harmonics SDPN, approximation of the neutron transport equation is proposed. The SDPN equations are derived from the multi-group DPN equations for N=1,2,3 (comparable to the SP3, SP5, and SP7 equations, respectively), and are converted into the form of second order multi-group diffusion equations. The finite element method with the variational approach is then used to numerically solve these equations. The computational performance of the SDPN method is compared with the SPN on several fixed-source and criticality test problems. The results show that the SDPN formulation generally results in parameters like criticality eigenvalue, disadvantage factors, absorption rate, etc. more accurately than the SPN, even up to an order of magnitude more precise, while the computational effort is the same for both methods.