Abstract/Details

Convergence analysis of the coarse mesh finite difference method


2003 2003

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Abstract (summary)

The convergence rates of the nonlinear coarse mesh finite difference (CMFD) and the coarse mesh rebalance (CMR) methods are derived analytically for one- and two-dimensional geometries and one- and two-energy group solutions of the fixed source diffusion problem in a non-multiplying infinite homogeneous medium. The derivation is 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 was shown to be a dominant parameter for the convergence rate and for the stability of the iterative algorithms. For a small mesh size problem, 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, one-node CMFD becomes unstable for large mesh sizes. To remedy this instability, an under-relaxation 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 under-relaxation parameter is analytically derived and the one-node CMFD with the optimum relaxation is shown to be unconditionally stable. Additional numerical analysis was performed on the convergence of each algorithm with the U.S. NRC Neutron Kinetics code PARCS. It was confirmed that the insights about the CMFD and the CMR methods obtained for simple model problems in Chapters 2–4 are valid for the realistic three-dimensional two-group eigenvalue and transient fixed source problems.

Indexing (details)


Subject
Nuclear physics
Classification
0552: Nuclear physics
Identifier / keyword
Applied sciences; Coarse-mesh finite-difference; Convergence; Discontinuity
Title
Convergence analysis of the coarse mesh finite difference method
Author
Lee, Deokjung
Number of pages
204
Publication year
2003
Degree date
2003
School code
0183
Source
DAI-B 65/03, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
Advisor
Downar, Thomas J.
University/institution
Purdue University
University location
United States -- Indiana
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3124175
ProQuest document ID
305306648
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/305306648/abstract
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