Canonical Implementation of Simplified Spherical Harmonics (SPL) in the Neutron Diffusion Code AZNHEX

Abstract

The SPL approximation has been used to improve the accuracy of neutron transport solvers and has been widely used thanks to the diffusion like equations that can be solved with traditional diffusion codes. The objective of this work is to extend the AZtlan Nodal HEXagonal (AZNHEX) diffusion code capabilities to include SPL approximation. For achieving this goal, an independent preprocessor has been developed to determine new specific neutronic parameters based on the canonical form of the SPL approximation. The SPL neutronic parameters are used to conform an extended system of diffusion like differential equations that can be discretized and solved numerically. The degree of SPL approximation defines the number of equations. Since the original AZNHEX code solves one diffusion equation by means of an algebraic system (matrix) with size depending on energy groups, an artificial increase in the number of energy groups allows to increase the matrix order by adding additional rows and columns to the original matrix depending on the SPL order, SP3 increases the matrix order by two times, SP5 three times and SP7 four times. Two exercises are presented. The initial one for verification purposes in which the effects of mesh refinement and increase of SPL approximation degree are presented and discussed. It was shown that the percentage error between successive SPL approximations reduces in a consistent manner as the order of SPL approximation increases. A second case is presented for validation against a transport code. In this case it was shown that keff values approach asymptotically to the transport solver solution as the SPL degree of approximation increases and as mesh is finer.