A general presentation of the SPH equivalence technique in non-fundamental mode cases

Abstract We developed a SPH equivalence technique in non-fundamental mode condition between a full-core model solved with the method of characteristics (MOC) in 2D and a simplified full-core diffusion model with two-group, finite-difference method over a pure Cartesian mesh. The MOC and diffusion calculations are performed with DRAGON5 and DONJON5 codes, respectively. An objective function is set as the root mean square (RMS) error (MOC-diffusion discrepancy) on absorption distribution and leakage rates defined over the macro-geometry in DONJON5. Three algorithms were developed to converge on the SPH factors in non-fundamental mode condition: a fixed point method, a pure Newton method for unconstrained optimization and a memory-limited Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method. We investigated the benefit of all these three techniques on a series of LEU-COMP-THERM-008 BAW Core-XI loadings. We observe convergence success for all numerical techniques considered in this study.