A Discontinuous Galerkin Finite Element Method based axial SN for the 2D/1D transport method

Abstract

The 2D/1D transport method is a prominent solver for the 3D Boltzmann equation due to its strong geometric capability. To pursue high accuracy, the discrete ordinate (SN) method for transport equation is a straightforward choice as the axial 1D solver instead of the traditional nodal expansion method (NEM) for diffusion equation. In practice, the axial SN solver is usually combined with the transverse leakage splitting method to deal with the negative source issue, which strongly affects the convergence of the 2D/1D method. However, transverse leakage splitting breaks the consistency of scalar fluxes between the 2D MOC and 1D SN equations. To solve this problem, a discontinuous Galerkin finite element method (DGFEM) for axial SN together with an improved 2D/1D transport approach is proposed in the present study to ensure that the scalar flux from the 1D axial solver is the same as that from the 2D solver. The accuracy, consistency and computational efficiency of the new scheme are evaluated using various well-known numerical problems, including heterogeneous assembly problem, KUCA benchmark, and C5G5-3D benchmark.