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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
2023 ANS Winter Conference and Expo
November 12–15, 2023
Washington, D.C.|Washington Hilton
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
NRC moves ahead on HALEU enrichment, rulemaking, and guidance
The Nuclear Regulatory Commission is requesting comments on the regulatory basis for a proposed rule for light water reactor fuel designs featuring high-assay low-enriched uranium (HALEU), including accident tolerant fuel (ATF) designs, and on draft guidance for the environmental evaluation of ATFs containing uranium enriched up to 8 percent U-235. Some of the HALEU feedstock for those LWR fuels and for advanced reactor fuels could be produced within the first Category II fuel facility licensed by the NRC—Centrus Energy’s American Centrifuge Plant in Piketon, Ohio. On September 21, the NRC approved the start of enrichment operations in the plant’s modest 16-machine HALEU demonstration cascade.
Bin Zhang, Liang Zhang, Cong Liu, Yixue Chen
Nuclear Science and Engineering | Volume 189 | Number 2 | February 2018 | Pages 120-134
Technical Paper | doi.org/10.1080/00295639.2017.1394085
Articles are hosted by Taylor and Francis Online.
Angular discretization errors inherent in the discrete ordinates method are a major problem, especially for localized source problems and problems with strongly absorbing media or large-volume void regions, where angular discretization errors would be totally unacceptable. This paper proposes a regional angular adaptive algorithm together with a goal-oriented error estimate to solve the SN equations. Standard angular adaptive refinement techniques are based on estimated local errors. We compare an interpolated angular flux value against a calculated value to generate local errors. The adaptive quadrature sets can be created by subdividing a spherical quadrilateral into four spherical subquadrilaterals that have positive weights and can be locally refined. Techniques for mapping angular fluxes from one quadrature set to another are developed to transfer angular fluxes on the interfaces of different spatial regions. To provide a better detector response, local errors are weighted by the importance of a given angular region toward the computational goal, providing an appropriate goal-oriented angular adaptivity. First collision source methods are employed to improve adjoint flux calculation accuracy. We tested the performance and accuracy of the proposed goal-oriented regional angular adaptive algorithm within the ARES code for a number of benchmark problems and present the results of a one-region test model and the Kobayashi benchmark problems. The reduction of angular number is at least one order of magnitude for adaptive refinement. The benchmarks demonstrate that the proposed goal-oriented adaptive refinement can achieve the same level of accuracy as the SN method, which has significantly higher computation cost. Thus, adaptive refinement is a viable approach for investigating difficult particle radiation transport problems.
