Finite element method solution of the simplified P3 equations for general geometry applications

The method and performance of a finite element method based simplified P3 code developed for generalized geometry applications are presented. The code takes the mesh data produced by an external general-purpose mesh generator. The weighted residual method with Galerkin weighting is directly applied to the two SP3 equations which were slightly modified to attain symmetry. The linear system for the global problem involving two unknown flux moments per node is obtained by summing up the elementwise weighted residual equations. The solution accuracy is examined for a suite of benchmark problems consisting of typical thermal and fast reactor problems together with the comparisons against the corresponding diffusion theory solutions. The effectiveness of the quadratic basis function is assessed as well against the linear function. It is demonstrated that the SP3 formulation is particularly beneficial for fast neutron systems.

► A SP3 code was developed using FEM for general applications not limited by preset geometry.
► Element data created by a generic mesh generator are used for geometrical flexibility.
► Demonstrates that accuracy improvement by SP3 over diffusion is particularly significant for fast reactors.
► Selective quadratic mapping is realized to deal with curved surfaces with for efficient meshing.
► The code can be useful in analyzing fast neutron systems.