Two-group diffusion theory based on separation of variables

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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 languageEnglish
Pages (from-to)1-16
Number of pages16
JournalAnnals of Nuclear Energy
Issue number1
StatePublished - 1 Jan 1988
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear Energy and Engineering


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