Partial current balance method: a local Green's function technique for the numerical solution of multidimensional neutron diffusion problems

A method based on a local integral formulation of the neutron diffusion equation is developed and evaluated. The standard differential form of the diffusion equation for each energy group is converted into a local integral equation using locally defined Green's functions for each volume element. The Green's functions used are those for equivalent volume elements in which only removal and diffusion can occur. Each volume element is coupled only to the physically adjacent volume elements; this coupling arises from the partial current continuity conditions imposed at the volume element interfaces. The group fluxes and interface partial currents are approximated by (independent) polynomial expansions for each volume element. A series of test problems is used to demonstrate the one- and two-dimensional computational capabilities of the partial current balance method. The results are compared to those obtained using the finite difference and finite element methods. The partial current balance technique is shown to yield a significant increase in the accuracy attainable for a given spatial partition relative to the comparison methods. Moreover, the partial current balance method is shown to be a more efficient solution technique for the test problems considered