A new stochastic implicit depletion scheme with combined nuclide-flux relaxation and a review of computational efficiency and accuracy for stochastic implicit depletion schemes

Depletion calculations using the Monte-Carlo method for neutron transport commonly suffer from numerical instabilities due to a phenomenon known as xenon-power oscillations. Such oscillations are physical in nature and are regularly observed in real nuclear reactors; but the feedback between spatial xenon concentration and the spatial power distribution in most Monte-Carlo depletion simulations is nonphysical and creates stability issues when depletion is modeled in optically thick problems such as full-length fuel assemblies or full cores. The equilibrium xenon approach or stochastic implicit (SI) depletion schemes are commonly used to ameliorate these issues as resolving xenon-power oscillations by simply increasing the number of simulated histories is usually an intractable approach. This study extends a previously proposed constant relaxation predictor–corrector SI approach (SI-CE/LI) by considering a new scheme with constant relaxation of both the spatial nuclide density and flux (or power) distributions. The new scheme is called the SI-CE/LI-Flux-Nuclide (SI-CE/LI-FN) scheme. Combined relaxation of both the spatial nuclide and flux distributions has a synergistic effect and the proposed methodology is able to obtain stable solutions to a 700 cm tall Fluoride-salt High temperature Reactor fuel assembly problem. With properly chosen relaxation factors, performance is equal, or better, than that of single-field relaxation approaches used in SI depletion schemes. Moreover, SI approaches offer a new way to split computational effort in already computationally intense depletion calculations; therefore, the apportioning of computational effort when using SI schemes is further investigated and practical guidance is given for users of SI depletion schemes.