A discontinuous heterogeneous finite element method for two-dimensional transport calculations

Discrete ordinate methods based on nodal or characteristics schemes for regular meshes provide fast solutions for transport problems in reactor physics, encompassing a wide range of applications, from fuel assembly to the whole core calculations. However, a drawback with these methods is that they require a pre-homogenization step in order to deal with cells containing fuel pins. In this work, a discontinuous heterogeneous finite element method (DHFEM) is presented and discussed. This method is intended for realistic numerical pin-by-pin lattice calculations, in which an exact representation of the geometric shape of the pins is made without homogenization. The method keeps the advantages of conventional discrete ordinate methods, such as fast execution together with the possibility to deal with a large number of spatial meshes, while minimizing the need for geometrical modeling. Further, the DHFEM provides a complete factorization in energy, space and angle for the discretized matrices and minimizes, thus, storage requirements. This particular feature makes the DHFEM an excellent candidate for 3-dimensional core transport calculations. A point that in itself justifies this study. An angular multigrid acceleration technique has also been developed to speed up the rate of convergence of the inner iterations. (authors)