Numerical stability of the predictor–corrector method in Monte Carlo burnup calculations of critical reactors

Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the simplest methods, such as the beginning-of-step and middle-of-step constant flux approximations, are numerically unstable in fuel cycle calculations of critical reactors. Here we show that even the predictor–corrector methods that are implemented in established Monte Carlo burnup codes can be numerically unstable in cycle calculations of large systems.

► The presence of feedback between the neutron flux and nuclide field can cause numerical instabilities in cycle calculations. ► Numerical stability of the predictor-corrector coupling schemes of existing Monte Carlo burnup codes was studied. ► The common predictor-corrector schemes are shown to be unstable in Monte Carlo burnup calculations.