{"title":"Application of Backward Differential Formula and Anderson’s method for multigroup diffusion transient equation","authors":"","doi":"10.1016/j.anucene.2024.110837","DOIUrl":null,"url":null,"abstract":"<div><p>This paper focuses on the application of the Backward Differential Formula (BDF) and Anderson’s method for neutron diffusion transient simulations. The B-spline finite element method is used for spatial discretization of continuous equations into the system of ODEs. BDF with adaptive step size and approximation order is used for integration of the ODEs over time. In-step multigroup equation is solved using the block Gauss–Seidel method, where the inner equation is solved using the ILU(0)-preconditioned Conjugate Gradient method. Anderson’s method is employed first to solve the in-step non-linear equation that couples the neutron and temperature models, and second, to accelerate the convergence of the block Gauss–Seidel algorithm. The performance of the time integration scheme and the in-step equation solver are verified on the point kinetics equation and two-dimensional benchmarks.</p></div>","PeriodicalId":8006,"journal":{"name":"Annals of Nuclear Energy","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0306454924005000/pdfft?md5=a13e72fcdccfdcad9ce166f8064cfbe8&pid=1-s2.0-S0306454924005000-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Nuclear Energy","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0306454924005000","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
Abstract
This paper focuses on the application of the Backward Differential Formula (BDF) and Anderson’s method for neutron diffusion transient simulations. The B-spline finite element method is used for spatial discretization of continuous equations into the system of ODEs. BDF with adaptive step size and approximation order is used for integration of the ODEs over time. In-step multigroup equation is solved using the block Gauss–Seidel method, where the inner equation is solved using the ILU(0)-preconditioned Conjugate Gradient method. Anderson’s method is employed first to solve the in-step non-linear equation that couples the neutron and temperature models, and second, to accelerate the convergence of the block Gauss–Seidel algorithm. The performance of the time integration scheme and the in-step equation solver are verified on the point kinetics equation and two-dimensional benchmarks.
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.
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