Development and Evaluation of a Discontinuous Galerkin Method in the DRAGON5 Code

Abstract

A Discontinuous Galerkin (DG) finite element method using Lagrange polynomials is presented for one- and two-dimensional Cartesian geometries. This method is developed up to high spatial orders (linear, parabolic and cubic) in the DRAGON5 code within the context of the discrete ordinates method for the resolution of the transport equation. This solver is then pitted against the already-implemented Diamond Differencing (DD) scheme on 1D/2D legacy benchmark problems. This paper, hence, aims to provide a comparison between DG and DD with respect to accuracy of results and rate of convergence on diffusive problems. The latter is evaluated in terms of number of scattering iterations and computational time. This work actually sits within a greater framework of developing an efficient finite element discrete ordinates solver in DRAGON5 for thermal and fast nuclear reactor problems. It was found that DG gives either more or as accurate results as DD, although taking more time to run. It was, however, found to be more robust in some cases.