Mixed-dual implementations of the simplified [formula omitted] method

Abstract

We present implementations of the Raviart–Thomas finite element method for solving the simplified P n approximation of the transport equation in 3-D geometries. This method can be applied to the full-core simulation of nuclear reactors with a regular Cartesian or hexagonal mesh. The Raviart–Thomas and Raviart–Thomas–Schneider methods are assuming a domain with Cartesian and hexagonal meshes, respectively. The Raviart–Thomas–Schneider method is based on a dual variational formulation defined over lozenge elements 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 selected benchmarks in 2- and 3-D geometry.