Fourier convergence analysis of two-dimensional/one-dimensional coupling methods for the three-dimensional neutron diffusion eigenvalue problems
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- Fourier convergence analysis of two-dimensional/one-dimensional coupling methods for the three-dimensional neutron diffusion eigenvalue problems
- Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook; Lee, Deokjung; Downar, Thomas J.
- Issue Date
- AMER NUCLEAR SOCIETY
- NUCLEAR SCIENCE AND ENGINEERING, v.156, no.1, pp.74 - 85
- The purpose of this paper is to present the Fourier convergence analysis of four methods for performing two-dimensional/one-dimensional (2-D/1-D) coupling to solve neutron diffusion eigenvalue problems (EVPs). The four methods differ principally in the manner of using the interface currents or node average fluxes to perform the 2-D/1-D coupling. Method A uses net currents, method B employs partial currents, method C uses a current correction factor, and method D uses an analytic expression for the axial net currents. In a previous paper, we analyzed the convergence behavior of these methods for the 2-D/1-D coupling of the fixed source problem (FSP). In this paper, the convergence performance of these methods is analyzed for the EVP using a one-group neutron diffusion EVP in a homogeneous infinite slab geometry. Among the four methods, method A diverges for small mesh sizes as it did in the FSP, whereas the other methods are stable regardless of the mesh size. The spectral radii of methods C and D are identical while the latter had a smaller spectral radius than the former in an FSP. The spectral radii of methods C and D are smaller than that of method B in the range of practical mesh size. The spectral radii approach one for all the methods as the mesh size increases, while in the FSP the spectral radii of method B approached a finite positive value and those of the other methods approached zero. For practical applications, method C has several advantages over the other methods and is the preferred 2-D/1-D coupling method for EVPs.
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