## Variable Fidelity Monte Carlo Neutron Transport: On Combining Multi-Group and Continuous Energy Representation in Monte Carlo Calculations

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## Abstract

This thesis investigates the feasibility of Monte Carlo (MC) neutronic calculations that combine multi-group (MG) and continuous energy (CE) representation of nuclear interaction data in different spatial regions. In general, MG MC calculations run 3-4 times faster than CE MC. Thus, it might be possible to reduce the calculation time without significant loss of accuracy, if the high fidelity CE representation is constrained to a small spatial region around an estimate of interest, while the rest of the domain is represented with a more efficient MG model. The possibility of combined MG-CE MC calculations has been suggested in the literature, but, until now, their feasibility has not been investigated in the context of eigenvalue calculations and separation of different fidelity regions in space.

It would have been difficult to obtain a working prototype of the combined MG-CE calculation using codes available to the reactor physics community, because MC codes are usually not designed with modification by a user in mind. Since this problem cannot be unique to this PhD project, a need for a MC neutron transport code optimised for prototyping of new methods was postulated. To address it, a new code called SCONE (Stochastic Calculator Of Neutron transport Equation) was written. In contrast to the established codes, it prioritises the ease of modification over computational performance. Its intended users are graduate students and researchers. SCONE relies on object-oriented architecture and is written in Fortran 2008. The work on SCONE is not yet finished, but, in its current state, its transport algorithms were successfully verified against Serpent for CE and analytical benchmarks for MG.

The error that may be introduced as a result of the combined MG-CE calculation was analysed in the framework of 1st order perturbation theory. Three distinct error categories were identified. One of them, unique to eigenvalue problems, is the normalisation error, which results from different criticality of MG and CE representations of the system. To remove this error, it is necessary to scale fission neutron production in the CE and MG regions by the criticalities that would have been obtained in single fidelity calculations. To obtain them, the fixed production ratio was proposed. It was shown to be effective for simple PWR problems with reflective boundary conditions.

The main difficulty for the design of the interface between MG and CE regions is the selection of an exact energy value for a particle crossing the boundary from MG to CE region. The selection was accomplished using methods derived from self-shielding calculations applied to a simplified pin cell model of a neighbourhood of the interface. This approach was successful at reducing a relatively large (4-7%) error in resonance capture rate in the CE region for simple problems, but the model may be inaccurate in the vicinity of heterogeneities in the reactor lattice, such as guide tubes or reflectors.

This thesis has demonstrated the feasibility of the combined MG-CE calculations. Furthermore, it has shown that the error introduced by the MG model to the CE result is manageable for problems where the difference between MG and CE model is most significant on small, intra-assembly scales. For problems where there is a significant difference in flux distribution between MG and CE on a large scale, the methods introduced in this thesis were found to be insufficient for estimates normalised to a reaction that spans the entire core (e.g. total power). However, if the normalisation is contained within the CE region (e.g. nodal code parameters), the error can be significantly improved with respect to a pure MG calculation. Furthermore, the combined MG-CE calculation can execute significantly faster than pure CE, but the magnitude of the acceleration is dependent on the MG region volume fraction in the MG-CE calculation. Also, a significant implementation overhead over a theoretical maximum (up to 30%) was observed. The results suggest that it may be attributed to inefficiencies in instruction and memory caching.