Pin-wise homogenization for SPN neutron transport approximation using the finite element method

The neutron transport equation describes the distribution of neutrons inside a nuclear reactor core. Homogenization strategies have been used for decades to reduce the spatial and angular domain complexity of a nuclear reactor by replacing previously calculated heterogeneous subdomains by homogeneous ones and using a low order transport approximation to solve the new problem. The generalized equivalence theory for homogenization looks for discontinuous solutions through the introduction of discontinuity factors at the boundaries of the homogenized subdomains. In this work, the generalized equivalence theory is extended to the Simplified PN equations using the finite element method. This extension proposes pin discontinuity factors instead of the usual assembly discontinuity factors and the use of the simplified spherical harmonics approximation rather than diffusion theory. An interior penalty finite element method is used to discretize and solve the problem using discontinuity factors. One dimensional numerical results show that the proposed pin discontinuity factors produce more accurate results than the usual assembly discontinuity factors. The proposed pin discontinuity factors produce precise results for both pin and assembly averaged values without using advanced reconstruction methods. Also, the homogenization methodology is verified against the calculation performed with reference discontinuity factors.