Multigroup application of the anisotropic FEM code FELTRAN to one, two, three-dimensions and R-Z problems

The multigroup even parity form of the neutron transport equation, with anisotropic scattering, has been solved by the Finite Element Method (FEM). The maximum principle for the even parity equation is employed. Spherical harmonics are used to represent the angular dependence of the flux and scattering while finite elements are used in the spatial domain. A finite element code, FELTRAN, has been developed which solves multigroup anisotropic scattering problems in one, two and three dimensions. Angular integrals which appear in the functional are evaluated in a general and modular form within the code; hence any desired order of anisotropic scattering and moments for the even parity flux can be chosen. In the spatial domain various types of elements are used for both regular and irregular geometries. Lagrangian linear, quadratic and cubic rectangular elements are used in X-Y and R-Z regular geometry, while curved geometries are handled by triangular elements. Solutions may also be obtained for the adjoint form of the even parity equation. Some representative examples in one, two and three dimensions are analysed and comparison is made with discrete-ordinates finite-difference codes ANISN and DOT, together with a 22-group problem intended to demonstrate the capabilities of FELTRAN in solving more practical problems.