Underlying mathematical relations for COMET calculations in problems with global symmetry

This paper derives the underlying mathematical relations for reactor core problems with global reflection and/or rotation symmetry within the context of COMET’s incident flux response expansion theory. The derivation rigorously establishes the relationships between the expansion moments of the incoming and outgoing partial current across coarse mesh surfaces and their corresponding symmetric surfaces under various scenarios in the core. These global (i.e., whole-core) symmetry relations are then integrated into the hybrid stochastic deterministic coarse mesh transport code COMET, enabling the new code to model a portion of reactor cores which have reflection and/or rotation symmetry without increasing the number of unique coarse meshes in the precomputation of the COMET response function library. The new COMET code is numerically validated in Cartesian and Hexagonal geometries by using two sets of problems, namely, a set of stylized PWR benchmark core configuration with 1/8th reflection symmetry and a set of three Advanced High Temperature Reactor (AHTR) core configurations with 120° rotation symmetry. Results from these benchmark calculations demonstrate that the core eigenvalues and fission density distributions predicted by modeling only a portion of the core using the global symmetry relations are in excellent agreement with the full core results as expected. The difference in the core eigenvalues varies from 0 to 2 pcm for both the PWR and AHTR benchmark problems. The average relative differences in the fission density distributions range from 0.012% to 0.014% and from 0.044% to 0.060% for the PWR and AHTR problems, respectively. All the discrepancies fall within three standard deviations of the corresponding COMET uncertainties. Additionally, it is found that modeling just the symmetric portion of the cores speed up COMET by eight and three times for the PWR and AHTR core configurations, respectively.