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Division Spotlight
Mathematics & Computation
Division members promote the advancement of mathematical and computational methods for solving problems arising in all disciplines encompassed by the Society. They place particular emphasis on numerical techniques for efficient computer applications to aid in the dissemination, integration, and proper use of computer codes, including preparation of computational benchmark and development of standards for computing practices, and to encourage the development on new computer codes and broaden their use.
Meeting Spotlight
2021 Student Conference
April 8–10, 2021
North Carolina State University|Raleigh Marriott City Center
Standards Program
The Standards Committee is responsible for the development and maintenance of voluntary consensus standards that address the design, analysis, and operation of components, systems, and facilities related to the application of nuclear science and technology. Find out What’s New, check out the Standards Store, or Get Involved today!
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Latest News
ANS Board of Directors votes to retire outdated position statements
The American Nuclear Society’s Board of Directors on November 19 voted to retire several outdated position statements, as requested by the Public Policy Committee. Among them are Position Statements #37 and #63, dating from 2010, which have been retired for lacking policy recommendations and for being redundant, as other position statements exist with language that better articulates the Society’s stance on those topics.
Hans R. Hammer, Jim E. Morel, Yaqi Wang
Nuclear Science and Engineering | Volume 193 | Number 5 | May 2019 | Pages 453-480
Technical Paper | dx.doi.org/10.1080/00295639.2018.1542865
Articles are hosted by Taylor and Francis Online.
In this paper we show the extension of nonlinear diffusion acceleration (NDA) to geometries containing small voids using a weighted-least-squares (WLS) high-order equation. Even though the WLS equation is well defined in voids, the low-order drift-diffusion equation was not defined in materials with a zero cross section. This paper derives the necessary modifications to the NDA algorithm. We show that a small change to the NDA closure term and a nonlocal definition of the diffusion coefficient solve the problems for void regions. These changes do not affect the algorithm for optically thick material regions while making the algorithm well defined in optically thin ones. We use a Fourier analysis to perform an iterative analysis to confirm that the modifications result in a stable and efficient algorithm. Later in the paper, numerical results of our method are presented. We test this formulation with a small, one-dimensional test problem. Additionally, we present results for a modified version of the C5G7 benchmark containing voids as a more complex, reactor-like problem. We compared our results to Texas A&M’s transport code PDT, utilizing a first-order discontinuous formulation as reference and the self-adjoint angular flux equation with void treatment (SAAF), a different second-order form. The results indicate that the NDA WLS performed comparably or slightly worse then the asymmetric SAAF while maintaining a symmetric discretization matrix.
