Numerical methods applied to pin power reconstruction based on coarse-mesh nodal calculation

Abstract

The proposed reconstruction processes combine the two-dimensional (2D) neutron diffusion equation discretized by finite difference method (FDM) and Galerkin finite element method (GFEM) with homogeneous flux distributions. The Finite Element Reconstruction Method (FERM) uses a homogeneous flux distribution over the extremities of each interval that constitute the faces of the fuel assembly (FA). In turns, the Finite Difference Reconstruction Method (FDRM) uses a homogeneous flux distribution over each interval that constitute the faces of the fuel assembly (FA). These flux distributions are obtained for each face of the FA from one-dimensional (1D) polynomial expansions. Such boundary conditions (flux distributions) are based on the average fluxes on the node faces, which are provided by the coarse-mesh nodal calculation performed in homogeneous nodes with dimensions of a FA. The Nodal Expansion Method (NEM) is used for nodal calculation and also provides the multiplication factor of the problem. These reconstruction methods use homogeneous nuclear parameters providing homogeneous flux distributions within the FA. The modulation method is applied to obtain heterogeneous distributions within the FA. To validate the results obtained by the reconstruction methods, such reconstructed heterogeneous distributions are compared with the reference values and with reconstruction performed by the PARCS code. The results show the good accuracy and efficiency of both methods.