Solution of 1-D multi-group time-dependent diffusion equations using the coupled reactors theory

A new method to solve time-dependent multi-group diffusion equations is presented using multi-point kinetics equations of the coupled reactors theory. The usual improved quasi-static method is generalized such that the fission sources for each core or node obtained from multi-point kinetics equations are used as amplitude functions for each node instead of a single amplitude function. Coupling coefficients between nodes were calculated exactly, and we found that the solution for a benchmark problem was in good agreement with the reference solution. It is shown that weakly coupled reactors of two cores can be well treated by a two-point model with constant coupling coefficients.