Stochastic semi-implicit substep method for coupled depletion Monte-Carlo codes

Abstract

Coupled Monte Carlo burnup codes aim to evaluate the time evolution of different parameters, such as nuclide densities, for accurate modeling of the different reactor designs and associated fuel cycles. Recently a major deficiency in numerical stability of existing Monte Carlo coupling schemes was identified. Alternative, stable coupling schemes were derived, implemented and verified. These methods are iterative and rely on either the end-or middle-of-step (MOS) reaction rates to evaluate the end-of-step (EOS) nuclide densities. Here, we demonstrate that applying the EOS methods for realistic problems may lead to highly inaccurate results. Considerable improvement can be made by adopting MOS method but the accuracy may still be insufficient. The solution proposed in this work relies on the substep method that allows reducing the time discretization errors. The proposed and tested substep method also assumes that the reaction rates are linear functions of the logarithm of the nuclide densities. The method was implemented in BGCore code and subsequently used to perform a series of test case calculations. The results demonstrate that better accuracy and hence efficiency can be achieved with negligible additional computational burden.

A perturbation-based susbtep method for coupled depletion Monte-Carlo codes

“…This, in turn, increases the overall calculation time. The same study (Kotlyar and Shwageraus, 2015) extends the method by incorporating a substep approach (Isotalo and Aarnio, 2011). The results indicated that introduction of substeps leads to substantial performance improvement compared to the previously suggested methods (Kotlyar and Shwageraus, 2014).…”

“…Alternative methods (Kotlyar and Shwageraus, 2014) were suggested to address the stability issues. These methods were then extended (Kotlyar and Shwageraus, 2015) to include a substep (Isotalo and Aarnio, 2011) approach, which allows accounting for the reaction rates variation within the depletion timestep. However, these methods typically require multiple iterations and additional neutron transport solutions to converge.…”

“…Therefore, new coupling methods have been developed for MC-burnup applications which also account for the dependence of reaction rates on thermal hydraulic conditions (Kotlyar and Shwageraus, 2014). Although these methods resolved the issue of numerical stability, further studies (Kotlyar and Shwageraus, 2015;Kotlyar and Shwageraus, 2016) indicated that computational efficiency of these methods may be questionable. In other words, the time discretization needs to be extremely fine to obtain accurate results.…”

Sub-step methodology for coupled Monte Carlo depletion and thermal hydraulic codes

“…Recent studies (Kotlyar and Shwageraus, 2016) indicated that the efficiency of the SIE may be quite poor. More specifically, in order to obtain accurate results, the time discretization steps are required to be extremely small, which increases the overall calculation time.…”

“…One of the options to improve the original SIE methods was to include a sub-step approach. Previous studies (Kotlyar and Shwageraus, 2016) introduced the sub-step methodology for coupled MC depletion solution and fixed TH conditions. The method was implemented in BGCore and used a log-linear correlation between the nuclide densities and reaction rates to better account for the variation in reaction rates within the time step.…”