Optimal time step length and statistics in Monte Carlo burnup simulations

Abstract

Monte Carlo burnup simulations continue to be seen as computationally very expensive numerical routines despite recent developments of associated methods. Here, we suggest a way of improving the computing efficiency via optimisation of the length of the time steps and the number of neutron histories that are simulated at each Monte Carlo criticality run. So far, users of Monte Carlo burnup codes have been required to set these parameters at will; however, an inadequate choice of these free parameters can severely worsen the computing efficiency. We have tested a large number of combinations of the free parameters on a simplified and fast solver, and we have observed that the computing efficiency was maximized when the computing cost of all Monte Carlo neutron transport calculations (summed over all time steps) was approximately comparable to costs of other procedures (all depletion simulations, the loading and processing of neutron cross sections, etc.). In this technical note, we demonstrate these results, and we also derive a simple theoretical model of the convergence of Monte Carlo burnup simulations that conforms to these numerical results. Here, we also suggest a straightforward way to automatise the selection of the optimal values of the free parameters for Monte Carlo burnup simulations.