Development and improvement of the quadratic depletion method

In nuclear reactor depletion calculations, the conventional predictor–corrector (PC) method requires two neutron transport calculations per burnup step. However, in high-fidelity calculations, these two transport calculations significantly reduce computational efficiency, especially for reactors reloaded with gadolinium (Gd)-bearing fuels, which require much finer depletion steps. The quadratic depletion (QD) method skips the corrector-step transport calculation and employs quadratic interpolation combined with a post-correction method to preserve accuracy. Nevertheless, the traditional QD method requires an excessive number of substeps to maintain precision for Gd-bearing systems, leading to high computational costs. To address this issue, a novel two-level predictor–corrector QD (TL-PC-QD) method is proposed to reduce the number of substeps. Comparative applications to Gd-bearing assembly and whole-core cases show that the TL-PC-QD method significantly reduces the number of substeps of the traditional QD method.