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55th annual Nuclear News Buyers Guide now available
For American Nuclear Society members and Nuclear News subscribers, the 2024 Buyers Guide is now available in the ANS Digital Nuclear Library. The print version will be mailed along with the May “Capacity Factors/Nuclear Security” issue of Nuclear News magazine.
The corresponding ANS online Buyers Guide database is available year-round to all readers—updated with the latest products, services, and suppliers contact information for more than 600 nuclear-related companies.
Hyun Chul Lee, Deokjung Lee, Thomas J. Downar
Nuclear Science and Engineering | Volume 151 | Number 1 | September 2005 | Pages 46-54
Technical Paper | doi.org/10.13182/NSE04-68
Articles are hosted by Taylor and Francis Online.
Two methods are proposed for solving the three-dimensional neutron diffusion equation by iterating between solutions of the two-dimensional (2-D) radial and one-dimensional (1-D) axial solutions. In the first method, the 2-D/1-D equations are coupled using a current correction factor (CCF) with the average fluxes of the lower and upper planes and the axial net currents at the plane interfaces. In the second method, an analytic expression for the axial net currents at the interface of the planes is used for planar coupling. A comparison of the new methods is made with two previously proposed methods, which use interface net currents and partial currents for planar coupling. A Fourier convergence analysis of the four methods was performed, and results indicate that the two new methods have at least three advantages over the previous methods. First, the new methods are unconditionally stable, whereas the net current method diverges for small axial mesh size. Second, the new methods provide better convergence performance than the other methods in the range of practical mesh sizes. Third, the spectral radii of the new methods asymptotically approach zero as the mesh size increases, while the spectral radius of the partial current method approaches a nonzero value as the mesh size increases. Of the two new methods proposed here, the analytic method provides a smaller spectral radius than the CCF method, but the CCF method has several advantages over the analytic method in practical applications.