A Raviart–Thomas–Schneider solution of the diffusion equation in hexagonal geometry

We present an implementation on the Raviart–Thomas–Schneider finite element method for solving the diffusion equation in hexagonal 3D geometry. This method is dedicated to full-core fuel management and design applications studies of nuclear reactors featuring an hexagonal mesh. The Raviart–Thomas–Schneider method is based on a dual variational formulation defined over lozenges with a Piola transformation of the polynomial basis. An efficient ADI numerical technique was set up to solve the resulting matrix system. Validation results are given for the hexagonal IAEA 2D benchmark and for two additional benchmarks related to the Monju core in 2D and 3D.