An Extension of the Nodal Green's Function Method for Reactor Analysis

A method is presented for calculating the nodal flux distribution and the pin power distribution, as well as the effective multiplication, in a nuclear power reactor described by the one-dimensional, two-group diffusion equation. The method is based on the use of Green's functions in a nodal reactor description, and it extends the work of previous authors by including burnup-induced heterogeneities and by calculating local pin power distributions from spatial flux distributions within the node obtained by piecewise polynomial interpolation. An advantage of the method is that one obtains power and exposure distributions at fine mesh points, while retaining the economy characteristic of solutions of the neutron diffusion equation in the nodal framework. In numerical calculations carried out on model problems, good agreement is achieved between the results of the extended nodal Green's function method and those obtained using the CITATION finite difference code.