{"title":"系统推导 GSP3(0) 方程,使用 GTIN 方法对其进行离散化,并开发可切换 SP3 至 GSP3(0) 中子传输求解器","authors":"Abhishek Mishra , Aditi Ray , Tej Singh","doi":"10.1016/j.pnucene.2024.105422","DOIUrl":null,"url":null,"abstract":"<div><div>The Generalized Simplified Spherical Harmonics (GSP<sub>N</sub>) method has drawn recent interest owing to the fact that theoretically, it is equivalent to the P<sub>N</sub> and does not rely on any assumption other than piecewise homogeneity. Its level wise approach to P<sub>N</sub> offers an agreeable balance between the accuracy and computational efficiency making it a valuable mathematical tool for analyzing neutron transport problems pertaining to nuclear engineering and reactor physics. The lowest level approximation for <em>N</em> = 3, expressed as <span><math><mrow><msubsup><mtext>GSP</mtext><mn>3</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup></mrow></math></span>, offers reducing the complexity while still capturing the essential physics. In the current work, <span><math><mrow><msubsup><mtext>GSP</mtext><mn>3</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup></mrow></math></span> equations are derived along with the interface and boundary conditions for linear anisotropic scattering. These equations are then discretized using the generalized transverse integration nodal method for a two-dimensional system of piecewise homogeneous rectangular regions. The discretization is done with an option kept for reducing the <span><math><mrow><msubsup><mtext>GSP</mtext><mn>3</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup></mrow></math></span> formalism to the conventional SP<sub>3</sub>. Subsequently, a computer code has been developed to solve these discretized equations in the multigroup structure for vacuum, reflective or albedo boundaries. At present, this switchable SP<sub>3</sub>/<span><math><mrow><msubsup><mtext>GSP</mtext><mn>3</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup></mrow></math></span> code has the capability of estimating <em>k</em>-eigenvalue and position dependent scalar neutron flux within a given two-dimensional rectangular geometry. The code has been verified by solving SP<sub>3</sub>, <span><math><mrow><msubsup><mtext>GSP</mtext><mn>3</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup></mrow></math></span> and other benchmark problems from available literature. The results obtained from our code demonstrate that <span><math><mrow><msubsup><mtext>GSP</mtext><mn>3</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup></mrow></math></span> is superior to the conventional SP<sub>3</sub> and comparable to the recently proposed SDP<sub>N</sub> (N = 1,2,3) [M. Nazari, A. Zolfaghari, M. Abbasi, Prog. Nucl. Energy, 2023; <strong>166</strong>, 104,933] in terms of accuracy as well as computation time.</div></div>","PeriodicalId":20617,"journal":{"name":"Progress in Nuclear Energy","volume":"177 ","pages":"Article 105422"},"PeriodicalIF":3.3000,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Systematic derivation of GSP3(0) equations, its discretization using GTIN method and development of a switchable SP3 to GSP3(0) neutron transport solver\",\"authors\":\"Abhishek Mishra , Aditi Ray , Tej Singh\",\"doi\":\"10.1016/j.pnucene.2024.105422\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The Generalized Simplified Spherical Harmonics (GSP<sub>N</sub>) method has drawn recent interest owing to the fact that theoretically, it is equivalent to the P<sub>N</sub> and does not rely on any assumption other than piecewise homogeneity. Its level wise approach to P<sub>N</sub> offers an agreeable balance between the accuracy and computational efficiency making it a valuable mathematical tool for analyzing neutron transport problems pertaining to nuclear engineering and reactor physics. The lowest level approximation for <em>N</em> = 3, expressed as <span><math><mrow><msubsup><mtext>GSP</mtext><mn>3</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup></mrow></math></span>, offers reducing the complexity while still capturing the essential physics. In the current work, <span><math><mrow><msubsup><mtext>GSP</mtext><mn>3</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup></mrow></math></span> equations are derived along with the interface and boundary conditions for linear anisotropic scattering. These equations are then discretized using the generalized transverse integration nodal method for a two-dimensional system of piecewise homogeneous rectangular regions. The discretization is done with an option kept for reducing the <span><math><mrow><msubsup><mtext>GSP</mtext><mn>3</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup></mrow></math></span> formalism to the conventional SP<sub>3</sub>. Subsequently, a computer code has been developed to solve these discretized equations in the multigroup structure for vacuum, reflective or albedo boundaries. At present, this switchable SP<sub>3</sub>/<span><math><mrow><msubsup><mtext>GSP</mtext><mn>3</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup></mrow></math></span> code has the capability of estimating <em>k</em>-eigenvalue and position dependent scalar neutron flux within a given two-dimensional rectangular geometry. The code has been verified by solving SP<sub>3</sub>, <span><math><mrow><msubsup><mtext>GSP</mtext><mn>3</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup></mrow></math></span> and other benchmark problems from available literature. The results obtained from our code demonstrate that <span><math><mrow><msubsup><mtext>GSP</mtext><mn>3</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup></mrow></math></span> is superior to the conventional SP<sub>3</sub> and comparable to the recently proposed SDP<sub>N</sub> (N = 1,2,3) [M. Nazari, A. Zolfaghari, M. Abbasi, Prog. Nucl. Energy, 2023; <strong>166</strong>, 104,933] in terms of accuracy as well as computation time.</div></div>\",\"PeriodicalId\":20617,\"journal\":{\"name\":\"Progress in Nuclear Energy\",\"volume\":\"177 \",\"pages\":\"Article 105422\"},\"PeriodicalIF\":3.3000,\"publicationDate\":\"2024-09-23\",\"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/S014919702400372X\",\"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/S014919702400372X","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}
Systematic derivation of GSP3(0) equations, its discretization using GTIN method and development of a switchable SP3 to GSP3(0) neutron transport solver
The Generalized Simplified Spherical Harmonics (GSPN) method has drawn recent interest owing to the fact that theoretically, it is equivalent to the PN and does not rely on any assumption other than piecewise homogeneity. Its level wise approach to PN offers an agreeable balance between the accuracy and computational efficiency making it a valuable mathematical tool for analyzing neutron transport problems pertaining to nuclear engineering and reactor physics. The lowest level approximation for N = 3, expressed as , offers reducing the complexity while still capturing the essential physics. In the current work, equations are derived along with the interface and boundary conditions for linear anisotropic scattering. These equations are then discretized using the generalized transverse integration nodal method for a two-dimensional system of piecewise homogeneous rectangular regions. The discretization is done with an option kept for reducing the formalism to the conventional SP3. Subsequently, a computer code has been developed to solve these discretized equations in the multigroup structure for vacuum, reflective or albedo boundaries. At present, this switchable SP3/ code has the capability of estimating k-eigenvalue and position dependent scalar neutron flux within a given two-dimensional rectangular geometry. The code has been verified by solving SP3, and other benchmark problems from available literature. The results obtained from our code demonstrate that is superior to the conventional SP3 and comparable to the recently proposed SDPN (N = 1,2,3) [M. Nazari, A. Zolfaghari, M. Abbasi, Prog. Nucl. Energy, 2023; 166, 104,933] in terms of accuracy as well as computation time.
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.