## Abstract

The solution of the 3-D, two-group, neutron diffusion equation is reduced to an iterative solution of 1-D algebraic equations for nodal fluxes. The reduction is enabled by the assumption that the flux is separable in x, y and z. Although the detailed flux distribution in a typical LWR environment is not separable, the assumption will nonetheless result in a very appropriate distribution of integrated nodal fluxes. In return, there is no need to approximate the functional (i.e. x) form of the transverse (i.e. y) leakage and the ensuing I-D equations are homogeneous. The theory replaces coupled transverse fluxes with bucklings as dependent variables, therefore along with the flux iteration, there is a buckling update. In some cases the update will be oscillatory, unless strong under-relaxation is used for all cases. Iteration acceleration is nevertheless regained by solving the homogeneous equations as weak-source inhomogeneous, and by using the iteration ratio to extrapolate the power distribution. The code NOXER (Nodal Diffusion by Flux Separation) applies the theory. The 2-D cross-core assembly powers of a PWR, calculated with one mesh per assembly, typically results with an average error of 1% and maximum error of 3%, compared with a high-order, fine-mesh, finite-element calculation. The IBM 4361 and CRAY1 XMP times for generating these results are, respectively, ∼5s and ∼0.25s for an 1 8 core symmetry.

Original language | English |
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Pages (from-to) | 1-16 |

Number of pages | 16 |

Journal | Annals of Nuclear Energy |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 1988 |

Externally published | Yes |

## ASJC Scopus subject areas

- Nuclear Energy and Engineering