High-precision eigenvalues of the neutron transport equation by the Carlvik method

IF 2.3 3区工程技术 Q1 NUCLEAR SCIENCE & TECHNOLOGY

Annals of Nuclear Energy Pub Date : 2025-07-02 DOI:10.1016/j.anucene.2025.111672

Paolo Saracco , Nicolò Abrate , Sandra Dulla , Piero Ravetto

引用次数: 0

Abstract

High-precision results for solutions of neutron transport problems are important as a guidance to code developers and to understand the impact of physical and numerical approximations. The aim of this work is the determination of the eigenvalues of the transport equation in plane geometry, reaching results as accurate as one may desire, with practically no limitation in the number of exact digits required. The method proposed by Carlvik is re-visited and implemented through appropriate analytical manipulations within the Mathematica™ framework, exploiting some specific features of this software to keep a full control of the numerical precision throughout the whole calculation procedure. The Wynn-

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acceleration scheme is also used to improve the convergence trend. Some selected high-precision results are presented to illustrate the performance of the algorithm.

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用Carlvik方法计算中子输运方程的高精度特征值

中子输运问题解的高精度结果对于代码开发人员和理解物理和数值近似的影响具有重要的指导意义。这项工作的目的是确定平面几何中输运方程的特征值，达到人们所期望的精确结果，实际上没有所需精确数字的数量限制。在Mathematica™框架内，通过适当的分析操作，重新访问并实现了carvik提出的方法，利用该软件的一些特定功能，在整个计算过程中保持对数值精度的完全控制。采用Wynn- i加速格式改善了收敛趋势。给出了一些高精度的结果来说明该算法的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Nuclear Energy 工程技术-核科学技术

CiteScore

4.30

自引率

21.10%

发文量

632

审稿时长

7.3 months

期刊介绍： Annals of Nuclear Energy provides an international medium for the communication of original research, ideas and developments in all areas of the field of nuclear energy science and technology. Its scope embraces nuclear fuel reserves, fuel cycles and cost, materials, processing, system and component technology (fission only), design and optimization, direct conversion of nuclear energy sources, environmental control, reactor physics, heat transfer and fluid dynamics, structural analysis, fuel management, future developments, nuclear fuel and safety, nuclear aerosol, neutron physics, computer technology (both software and hardware), risk assessment, radioactive waste disposal and reactor thermal hydraulics. Papers submitted to Annals need to demonstrate a clear link to nuclear power generation/nuclear engineering. Papers which deal with pure nuclear physics, pure health physics, imaging, or attenuation and shielding properties of concretes and various geological materials are not within the scope of the journal. Also, papers that deal with policy or economics are not within the scope of the journal.