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Lee, Deokjung
Computational Reactor physics & Experiment lab (CORE Lab)
Research Interests
  • Reactor Analysis computer codes development
  • Methodology development of reactor physics
  • Nuclear reactor design(SM-SFR,PWR and MSR)

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Convergence analysis of the nonlinear coarse-mesh finite difference method for one-dimensional fixed-source neutron diffusion problem

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Title
Convergence analysis of the nonlinear coarse-mesh finite difference method for one-dimensional fixed-source neutron diffusion problem
Author
Lee, DeokjungDownar, TJKim, Y
Issue Date
2004-06
Publisher
AMER NUCLEAR SOCIETY
Citation
NUCLEAR SCIENCE AND ENGINEERING, v.147, no.2, pp.127 - 147
Abstract
The convergence rates of the nonlinear coarse-mesh finite difference (CMFD) method and the coarse-mesh rebalance (CMR) method are derived analytically for one-dimensional, one-group solutions of the fixed-source diffusion problem in a nonmultiplying infinite homogeneous medium. The derivation was performed by linearizing the nonlinear algorithm and by applying Fourier error analysis to the linearized algorithm. The mesh size measured in units of the diffusion length is shown to be a dominant parameter for the convergence rate and for the stability of the iterative algorithms. For a small mesh size problem, the nonlinear CMFD is shown to be a more effective acceleration method than CMR. Both CMR and two-node CMFD algorithms are shown to be unconditionally stable. However, the one-node CMFD becomes unstable for large mesh sizes. To remedy this instability, an underrelaxation of the current correction factor for the one-node CMFD method is successfully introduced, and the domain of stability is significantly expanded. Furthermore, the optimum underrelaxation parameter is analytically derived, and the one-node CMFD with the optimum relaxation is shown to be unconditionally stable.
URI
https://scholarworks.unist.ac.kr/handle/201301/7407
URL
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=3042552564
ISSN
0029-5639
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