Home / Store / Journals / Electronic Articles / Nuclear Science and Engineering / Volume 163 / Number 1
R. Le Tellier, D. Fournier, J. M. Ruggieri
Nuclear Science and Engineering
Volume 163 / Number 1 / September 2009 / Pages 34-55
Format:electronic copy (download)
This paper describes a new approach for treating the energy variable of the neutron transport equation in the resolved resonance energy range. The aim is to avoid recourse to a case-specific spatially dependent self-shielding calculation when considering a broad group structure. This method consists of a discontinuous Galerkin discretization of the energy using wavelet-based elements. A t-orthogonalization of the element basis is presented in order to make the approach tractable for spatially dependent problems.First numerical tests of this method are carried out in a limited framework under the Livolant-Jeanpierre hypotheses in an infinite homogeneous medium. They are mainly focused on the way to construct the wavelet-based element basis. Indeed, the prior selection of these wavelet functions by a thresholding strategy applied to the discrete wavelet transform of a given quantity is a key issue for the convergence rate of the method. The Canuto thresholding approach applied to an approximate flux is found to yield a nearly optimal convergence in many cases. In these tests, the capability of such a finite element discretization to represent the flux depression in a resonant region is demonstrated; a relative accuracy of 10-3 on the flux (in L2-norm) is reached with less than 100 wavelet coefficients per group.
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