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

Cited 19 time in webofscience Cited 0 time in scopus
  • Hit : 236
  • Download : 0
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 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 underrelaxation parameter is analytically derived, and the one-node CMFD with the optimum relaxation is shown to be unconditionally stable.
Publisher
AMER NUCLEAR SOC
Issue Date
2004-06
Language
English
Article Type
Article
Keywords

NODAL EXPANSION METHOD; EQUIVALENCE THEORY; STABILITY ANALYSIS; ITERATION; ACCELERATION; FORMULATION; EQUATIONS

Citation

NUCLEAR SCIENCE AND ENGINEERING, v.147, no.2, pp.127 - 147

ISSN
0029-5639
URI
http://hdl.handle.net/10203/85415
Appears in Collection
NE-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 19 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0