Underlying mathematical relations for efficient COMET response expansion coefficient and core calculations

The coarse mesh transport code COMET, a hybrid stochastic-deterministic neutronics solver with formidable computation speed, can provide high fidelity transport solutions to various reactor core problems. In this paper, to take advantage of local rotational and reflection symmetry existing in many reactor cores (e.g., fuel lattices and reflector blocks), the underlying mathematical relations among the response expansion coefficients of symmetric coarse meshes are developed to further improve the computational efficiency in both COMET response expansion coefficient generation and core calculation. This is done by a rigorous derivation of the transformation matrices for the angular and spatial expansion moments resulting from a rotation of a coarse mesh by an arbitrary angle or reflection of a coarse mesh. As a result, the relations for the response expansion coefficients of a coarse mesh with rotational symmetry can be then written as the Kronecker product of those transformation matrices. For coarse meshes with reflection symmetry, the sparse property, the outgoing surface symmetry property and the incident surface symmetry property of response expansion coefficients are rigorously derived. These underlying mathematical relations are implemented into COMET and evaluated on three stylized 3D PWR whole core benchmark problems. The COMET results using the response expansion coefficient library based on the underlying mathematical relations were compared to those using the library directly generated by Monte Carlo for all surfaces. It was found that the eigenvalues as well as the pin and assembly fission densities using the two libraries are in statistical agreement as expected. This indicates that the new COMET using the underlying mathematical relations maintains the high fidelity of the original COMET while improving computational efficiency by 10.7 and 3.7 times for COMET response expansion coefficient generation and core calculation, respectively. This also reduces the size of the library by 10.7 times.