Precise 3D reactor core calculation using Spherical Harmonics and Discontinuous Galerkin Finite Element Methods

Kenneth Assogba (1, 2) , Lahbib Bourhrara (1) , Igor Zmijarevic (1) , Grégoire Allaire (2)

1 SERMA - Service d’Études des Réacteurs et de Mathématiques Appliquées
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We study the use of PN method in angle and Discontinuous Galerkin in space to solve 3D neutron transport problem. PN method consists in developing the angular flux on truncated spherical harmonics basis. In this paper, we couple this method with the discontinuous finite elements in space to obtain a complete discretisation of the multigroup neutron transport equation. To investigate its precision, the method was applied to Takeda and C5G7 benchmark problems. These calculations point out that the proposed PN-DG method is capable of producing accurate solutions in small computational time, and that it is able to handle complex 3D geometries.

Mots clés: PN method; DG FEM; Discontinuous finite element method; neutron transport equation

Domaines: Analyse numérique [math.NA]; Physique Numérique [physics.comp-ph]; Equations aux dérivées partielles [math.AP]; Calcul parallèle, distribué et partagé [cs.DC]

Kenneth Assogba, Lahbib Bourhrara, Igor Zmijarevic, Grégoire Allaire. Precise 3D reactor core calculation using Spherical Harmonics and Discontinuous Galerkin Finite Element Methods. PHYSOR 2022 - International Conference on Physics of Reactors 2022, May 2022, Pittsburgh, United States. pp.1224-1233, ⟨10.13182/PHYSOR22-37354⟩. ⟨hal-03878111⟩