Comparison of two Subgroup Methods based on the Physical Probability Tables

This paper compares numerically two subgroup methods based on the use of physical probability tables as quadrature formula. The methods are denoted SG-GR and SG-IR because they are subgroup methods respectively relying on the General Resonance model and the Intermediate Resonance approximation. The SG-GR is the legacy self-shielding method in use in the APOLLO3^® lattice code, though it is usually employed with the mathematical probability tables and with a fine energy discretization (nearly 400 groups). The first numerical results on typical LWR calculations show that although the accuracy is satisfying with finer energy meshes, it rapidly decreases with a coarse energy mesh, for example, 69 groups. The SG-IR is a known subgroup method but had never been implemented in APOLLO3^®. A recent effort has been made to implement this method to the code on a coarse 69 group energy mesh. The preliminary study shows that the SG-IR method associated with the resonant cross-section based physical probability tables gives interesting results. Even though we are at an early stage of the development of the SG-IR method, many adjustments remain to be made, but the results are already encouraging.