Extending Gout's Wachspress finite elements on regular hexagons to higher orders

Considering a spatial discretization of the discrete ordinate transport equation based on a Discontinuous Galerkin upwind scheme, this paper presents the extension of Gout's Wachspress finite elements for honeycomb meshes to higher orders. Actually, a genuine method heavily relying on computational algebra is reported to evaluate rational finite elements on any type of convex polygons (with m sides) for any order k < m. It is an extension of finite elements proposed by Gout for pentagons and hexagons for a limited set of orders (typically, only up to 3 for the hexagon). The rationale behind this work is that core neutron transport simulations in a multiphysics coupling context (e.g. severe accident analysis for fast neutron reactors) are often performed with homogenized assemblies and reducing the associated computational time is necessary to make such highly-demanding simulations tractable. Considering a honeycomb core geometry, a spatial discretization based on high-order finite elements without subdivision of the hexagons into triangles or lozenges is an attempt at improving the trade-off between accuracy and computational resources. As a first step towards the application of such finite elements to neutron transport simulation, results for a one-group honeycomb benchmark are reported and compared with calculations performed with APOLLO3/MINARET solver based on a Discontinuous Galerkin upwind scheme over triangular meshes. (authors)