Efficient Coupled Transport-Depletion Sequence Using Hybrid Monte Carlo-Reduced Order Scheme

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Johnson, Andrew
Kotlyar, Dan
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In nuclear engineering, the topic of depletion involves modeling time-dependent material compositions in a nuclear system, such as a power plant. During operation, isotopes decay and are transmuted according to local reaction rates, leading to a constantly changing nuclide inventory. Modern analysis tools employ a two-step approach, where steady state neutron transport solutions are coupled with depletion solvers. By assuming constant reaction rates over a time step, coupling schemes do not accurately model the time dependence needed to capture the time-evolution of compositions. Furthermore, prohibitively small time steps must be used for some problems (e.g. 3D core), else numerical instabilities and oscillations may arise. In this research, a hybrid approach has been developed, implemented and tested. The method utilizes reduced-order methods to deplete at sub-intervals between high-fidelity Monte Carlo simulations. The reduced-order simulations obtain reaction rates that better reflect the spatial and temporal neutron flux distributions, without many expensive transport solutions. This fine time scale greatly reduces and in some cases eliminates the oscillatory behavior for instability-prone problems. In such cases, the hybrid method leads to a tenfold increase in accuracy. If the reduced-order solver is orders of magnitude faster than the Monte Carlo solver, this increase is obtained for little to no computational cost. This hybrid scheme has been implemented and tested using a custom framework, with an extensible interface for additional transport solvers. By holding a reactor model in memory, both high-fidelity and reduced-order methods can fully represent the problem in a consistent manner. The framework and the hybrid method contained therein have been compared to a stability limited test case and a practical reactor engineering problem, both demonstrating the tangible benefits of this novel coupling scheme.
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