Teaching the SN method: Zero to international benchmark in six weeks

Abstract

The discrete ordinates or SN method is employed to solve the neutron transport equation in a number of code packages that are considered mainstays of reactor design and safety analysis. Yet students often begin using these codes without having gained the deep understanding of the SN approach that stems from implementing the SN algorithm in a computer code of their own design. This paper presents a series of lectures and computing activities involving beginning graduate students having no prior transport theory experience. The students wrote three codes: a multigroup spatially homogenized code, an SN code in one-dimensional slab geometry and an SN code in two dimensional cartesian geometry. Accurate group cross sections and Legendre moments are essential for high-fidelity calculation; therefore, the students were also taught to use NJOY991 to generate appropriately weighted and energy self-shielded group constants. MATLAB code and NJOY99 script templates are presented for each of these activities. The students validated their final SN codes against an infinite-lattice pressurized water reactor (PWR) benchmark developed by the Organization for Economic Cooperation and Development Nuclear Energy Agency (OECD NEA). Good agreement - within a few percent on multiplication factors, spectra, and neutron interaction rates by species - was obtained. The students came away with self-authored, easily generalized SN algorithms and, more importantly, deeper confidence and understanding when using commercial S N codes in their own research.