Development of the nodal collocation method for solving the neutron diffusion equation

Abstract

The nodal collocation method is a new technique for the discretization of the multidimensional neutron diffusion equation where the solution sought is expressed in the form of tensorial expansions of Legendre polynomials defined over homogeneous parallelepipeds. In this study, we have truncated the tensorial expansions using the serendipity approximation in an attempt to reduce the total number of unknowns and improve the effectiveness of the discretization. The remaining Legendre coefficients are then determined in order to preserve selected moments of the neutron conservation equation in each parallelepiped. This approach allows a variable order of convergence without sacrificing the consistency peculiar to full tensorial expansions and generates matrix systems which may be resolved by an Alternating Direction Implicit algorithm. Furthermore, we have proved that the linear nodal collocation method and the mesh centered finite difference method are equivalent. Validation results are given for the IAEA 2-D and 3-D benchmarks and for a 2-D representation of a pressurized water reactor (PWR).