ANOVA-HDMR structure of the higher order nodal diffusion solution

Conference · Mon Jul 01 04:00:00 EDT 2013

OSTI ID:22212903

Bokov, P. M.; Prinsloo, R. H.; Tomasevic, D. I. ^[1]

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1. South African Nuclear Energy Corporation - Necsa, Building 1900, P.O. Box 582, 0001 Pretoria (South Africa)

Nodal diffusion methods still represent a standard in global reactor calculations, but employ some ad-hoc approximations (such as the quadratic leakage approximation) which limit their accuracy in cases where reference quality solutions are sought. In this work we solve the nodal diffusion equations utilizing the so-called higher-order nodal methods to generate reference quality solutions and to decompose the obtained solutions via a technique known as High Dimensional Model Representation (HDMR). This representation and associated decomposition of the solution provides a new formulation of the transverse leakage term. The HDMR structure is investigated via the technique of Analysis of Variance (ANOVA), which indicates why the existing class of transversely-integrated nodal methods prove to be so successful. Furthermore, the analysis leads to a potential solution method for generating reference quality solutions at a much reduced calculational cost, by applying the ANOVA technique to the full higher order solution. (authors)

• Research Organization: American Nuclear Society, 555 North Kensington Avenue, La Grange Park, IL 60526 (United States)
• OSTI ID: 22212903
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ACCURACY
APPROXIMATIONS
DIFFUSION EQUATIONS
MATHEMATICAL SOLUTIONS