Multischeme equivalence procedure for neutron transport finite element methods

Abstract Diffusion equivalence theory applied at the full-core level is well understood and enables preservation of the multiplication factor and key reaction rates. In many cases, however, high-interest regions inside the reactor benefit from a heterogeneous representation solved using a transport scheme. This paper formalizes the multischeme (MS) equivalence procedure in which the capability to use distinct transport operator approximations in different parts of the domain is combined with an equivalence procedure, thus enforcing preservation of the reaction rates in—and (optionally) leakage rates out of—the low-resolution domains, using Super Homogenization (SPH) and discontinuity factors (DFs). Two approaches are proposed: MS-SPH applies SPH factors to the diffusion interface terms, whereas MS-SPH-DF relies on DFs to enforce preservation of the net currents at the interface—in which case, one normalization factor per energy group and connected region is required. The main targeted applications of multischeme equivalence are (1) more accurate reaction rates inside the heterogeneous region and (2) the ability to rely on methods otherwise incompatible with equivalence. Both proposed methods can successfully reproduce the eigenvalue and reaction rates in the heterogeneous region. Although MS-SPH-DF may better capture local effects with very refined meshes, MS-SPH otherwise seems more appealing, due to its comparable accuracy with coarser meshes and its significantly reduced burden on the analyst for large applications, as reference currents are not needed. When global quantities of interest are specifically targeted (e.g., control rod worth), neither method appears superior to a standard, spatially restricted SPH approach.