A New Method for the Solution of Group Diffusion Equations

Abstract

The diffusion equations associated with the multigroup, multiregion problem are solved by expansions in eigenfunctions which are solutions of the Helmholtz equation. A determinantal criticality equation is exhibited in which the order of the determinant is independent of the number of groups and which can be solved without recourse to complicated computational procedures. Moreover, the need to fulfill explicitly the requirements that the flux and current associated with each neutron group be continuous across interfaces is eliminated.