Extending the finite elements neutronic code FENNECS to the Discontinuous Galerkin method

Abstract

The finite element method (FEM) neutronics code FENNECS was originally developed at GRS for unstructured geometry and first applied to fast reactors. It has recently been applied to light water reactors (LWRs). Indeed, most of the currently envisaged Small modular reactors (SMRs) concepts are based on well-proven LWR techniques. However, significant discrepancies were observed in terms of power distribution for the FENNECS prediction. The identified limitation is due to the implementation of the continuous Galerkin (CG) method, which enforces flux continuity between elements. This is incorrect due to the cross-section homogenization process. To overcome this problem, discontinuity factors can be introduced to allow for a more accurate description of the physics in LWR. Within the FEM frameworks, the modelling of discontinuous variables can be introduced using the discontinuous Galerkin (DG) formalism. FENNECS has been extended with the implementation of a new method based on the DG method. The method’s verification and validation were successfully achieved by comparing the assembly power distribution with a reference Monte Carlo solution for the NuScale SMR benchmark. Compared to the continuous approach, the discrepancies were significantly reduced from 20% to less than 4%.