求解希什金网格上尖锐层的中子输运问题

IF 3.2 3区工程技术 Q1 NUCLEAR SCIENCE & TECHNOLOGY

Progress in Nuclear Energy Pub Date : 2025-03-19 DOI:10.1016/j.pnucene.2025.105732

Tseelmaa Byambaakhuu, Dean Wang

{"title":"求解希什金网格上尖锐层的中子输运问题","authors":"Tseelmaa Byambaakhuu, Dean Wang","doi":"10.1016/j.pnucene.2025.105732","DOIUrl":null,"url":null,"abstract":"<div><div>If there exist sharp boundary layers and/or interior layers in the solution of neutron transport problems, numerical instability and oscillations may occur when the mesh is not fine enough around the sharp layers. In this work, we propose to solve the S<sub><em>N</em></sub> neutron transport equation by resolving the sharp boundary and interior layers with the piecewise uniform Shishkin mesh. The challenge is to determine the layer thickness for the transition point of the Shishkin mesh. We derive a mathematical expression for calculating the layer thickness based on the eigenvalues of the S<sub><em>N</em></sub> transport equation. Numerical results for the diamond difference (DD) and discontinuous Galerkin (DG) methods, are presented to show the improvement in the accuracy, stability, and efficiency with the Shishkin mesh.</div></div>","PeriodicalId":20617,"journal":{"name":"Progress in Nuclear Energy","volume":"185 ","pages":"Article 105732"},"PeriodicalIF":3.2000,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solving neutron transport problems with sharp layers on the Shishkin mesh\",\"authors\":\"Tseelmaa Byambaakhuu, Dean Wang\",\"doi\":\"10.1016/j.pnucene.2025.105732\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>If there exist sharp boundary layers and/or interior layers in the solution of neutron transport problems, numerical instability and oscillations may occur when the mesh is not fine enough around the sharp layers. In this work, we propose to solve the S<sub><em>N</em></sub> neutron transport equation by resolving the sharp boundary and interior layers with the piecewise uniform Shishkin mesh. The challenge is to determine the layer thickness for the transition point of the Shishkin mesh. We derive a mathematical expression for calculating the layer thickness based on the eigenvalues of the S<sub><em>N</em></sub> transport equation. Numerical results for the diamond difference (DD) and discontinuous Galerkin (DG) methods, are presented to show the improvement in the accuracy, stability, and efficiency with the Shishkin mesh.</div></div>\",\"PeriodicalId\":20617,\"journal\":{\"name\":\"Progress in Nuclear Energy\",\"volume\":\"185 \",\"pages\":\"Article 105732\"},\"PeriodicalIF\":3.2000,\"publicationDate\":\"2025-03-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Progress in Nuclear Energy\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0149197025001301\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"NUCLEAR SCIENCE & TECHNOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Progress in Nuclear Energy","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0149197025001301","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"NUCLEAR SCIENCE & TECHNOLOGY","Score":null,"Total":0}

引用次数: 0

摘要

在中子输运问题的求解中，如果存在尖锐的边界层和（或）内层，当尖锐层周围网格不够精细时，可能会出现数值不稳定和振荡。在这项工作中，我们提出了用分段均匀希什金网格解析尖锐边界层和内层来求解SN中子输运方程。挑战在于确定Shishkin网格过渡点的层厚度。根据SN输运方程的特征值，导出了计算层厚的数学表达式。给出了金刚石差法（DD）和不连续伽辽金法（DG）的数值计算结果，表明使用Shishkin网格可以提高精度、稳定性和效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Solving neutron transport problems with sharp layers on the Shishkin mesh

If there exist sharp boundary layers and/or interior layers in the solution of neutron transport problems, numerical instability and oscillations may occur when the mesh is not fine enough around the sharp layers. In this work, we propose to solve the S_N neutron transport equation by resolving the sharp boundary and interior layers with the piecewise uniform Shishkin mesh. The challenge is to determine the layer thickness for the transition point of the Shishkin mesh. We derive a mathematical expression for calculating the layer thickness based on the eigenvalues of the S_N transport equation. Numerical results for the diamond difference (DD) and discontinuous Galerkin (DG) methods, are presented to show the improvement in the accuracy, stability, and efficiency with the Shishkin mesh.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Progress in Nuclear Energy 工程技术-核科学技术

CiteScore

5.30

自引率

14.80%

发文量

331

审稿时长

3.5 months

期刊介绍： Progress in Nuclear Energy is an international review journal covering all aspects of nuclear science and engineering. In keeping with the maturity of nuclear power, articles on safety, siting and environmental problems are encouraged, as are those associated with economics and fuel management. However, basic physics and engineering will remain an important aspect of the editorial policy. Articles published are either of a review nature or present new material in more depth. They are aimed at researchers and technically-oriented managers working in the nuclear energy field. Please note the following: 1) PNE seeks high quality research papers which are medium to long in length. Short research papers should be submitted to the journal Annals in Nuclear Energy. 2) PNE reserves the right to reject papers which are based solely on routine application of computer codes used to produce reactor designs or explain existing reactor phenomena. Such papers, although worthy, are best left as laboratory reports whereas Progress in Nuclear Energy seeks papers of originality, which are archival in nature, in the fields of mathematical and experimental nuclear technology, including fission, fusion (blanket physics, radiation damage), safety, materials aspects, economics, etc. 3) Review papers, which may occasionally be invited, are particularly sought by the journal in these fields.