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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 SN codes in their own research.

1. Introduction

With the emergence of high-performance computing as an everyday, widely-used tool, Monte Carlo approaches to solving the neutron transport equation have become ascendant in both the classroom and the research arena. Monte Carlo codes offer the advantage of direct, exact solution of the transport equation with accuracy limited only by the fidelity of nuclear data and the availability of computing power. Hence other methods for solving the transport equation – discrete ordinates (SN), collision probability and integral approaches – while still in wide use are perhaps no longer being as intensively developed. This shift extends to the classroom in the sense that it is often easier to teach students to use Monte Carlo code packages especially when the system being studied contains irregular geometries.

It can be argued that, since even PhD students will be unlikely to be called upon to develop their own deterministic transport software during the course of their careers, teaching these methods from other than a theoretical standpoint is not productive. On the other hand, it is very likely that these students will be called upon to make use of a ‘legacy’ deterministic transport code. A number of codes that use the discrete ordinates approximation to the transport equation remain in widespread use; this method remains a very strong choice when systems having regular lattice geometries or systems in which neutron populations in regions of space and/or energy vary by

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Schneider, E. (2008, June), Teaching The Sn Method: Zero To International Benchmark In Six Weeks Paper presented at 2008 Annual Conference & Exposition, Pittsburgh, Pennsylvania. 10.18260/1-2--3428