Derivation of a stable coupling scheme for Monte Carlo burnup calculations with the thermal-hydraulic feedback

Numerically stable Monte Carlo burnup calculations of nuclear fuel cycles are now possible with the previously derived Stochastic Implicit Euler method based coupling scheme. In this paper, we show that this scheme can be easily extended to include the thermal-hydraulic feedback during the Monte Carlo burnup simulations, while preserving its unconditional stability property. At each time step, the implicit solution (for the end-of-step neutron flux, fuel nuclide densities and thermal-hydraulic conditions) is calculated iteratively by the stochastic approximation; the fuel nuclide densities and thermal-hydraulic conditions are iterated simultaneously. This coupling scheme is derived as stable in theory; i.e., its stability is not conditioned by the choice of time steps.