{"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":"2025-07-01","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":"2025/3/19 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"NUCLEAR SCIENCE & TECHNOLOGY","Score":null,"Total":0}
引用次数: 0
Abstract
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 SN 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 SN 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.
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.
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