Discontinuity factors for 1D PN equations using a Finite Element Method

Paper in proceeding, 2017

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 defines discontinuity factors at the boundaries of the homogenized subdomains. In this work, the generalized equivalence theory is extended to the PN equations for one-dimensional geometries using the finite element method. Here, pin discontinuity factors are proposed instead of the usual assembly discontinuity factors and the use of the spherical harmonics approximation as an extension of the diffusion theory. An interior penalty finite element method is used to discretize and solve the problem using discontinuity factors. 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. The homogenization methodology is also verified with the calculation of reference discontinuity factors.