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

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.