Property Discontinuities in the Solution of Finite Difference Approximations to the Neutron Diffusion Equations

The problem of representing discontinuous properties in a finite difference approximation to the Neutron Diffusion Theory is considered. The exact interface conditions in one dimension are approximated with the second order finite differences and integrotion over a second order expansion of the flux either side of the interface. Through this approach the problem of abrupt changes in the diffusion coefficient D is addressed. Nonuniformity of properties between regions is described by a five point equation, instead of the usual three point interior equation for uniform properties. Subsequently the five point equation is reduced to a three point equation. The resulting equation is not exactly equivalent to the conventional three point finite difference equation for uniform properties. The difference between them is shown to be negligible if sufficiently small steps are taken with explicit results for selected accuracy. Hence with sufficient nodal points and by averaging the coefficient D and the source term DE2 at an interface, the method is able to model flux variation between two different homogeneous regions.