Axial expansion methods for solution of the multi-dimensional neutron diffusion equation

The feasibility and practical implementation of axial expansion methods for the solution of the multi-dimensional multigroup neutron diffusion (MGD) equations is investigated. The theoretical examination which is applicable to the general MGD equations in arbitrary geometry includes the derivation of a new weak (reduced) form of the MGD equations by expanding the axial component of the neutron flux in a series of known trial functions and utilizing the Galerkin weighting. A general two-group albedo boundary condition is included in the weak form as a natural boundary condition. The application of different types of trial functions is presented