A novel boundary element method for nonuniform neutron diffusion problems

An advanced boundary element formulation has been proposed to solve the neu tron diffusion equation (NDE) for a 'nonuniform' system. The continuous spa tial distribution of a nuclear constant is assumed to he described using a polynomial function, Part of the constant term in the polynomial is left on the left-hand-side of the NDE, while the remainding is added to the fissio n source term on the right,hand-side to create a fictitious source. When th e neutron flux is also expanded using a polynomial, the boundary integral e quation corresponding to the NDE contains a domain integral related to the polynomial source. This domain integral is transformed into an infinite ser ies of boundary integrals, by repeated application of the particular soluti on for a Poisson-type equation with the polynomial source. In two-dimension al, one-group test calculations for rectangular domains, the orthogonality of Legendre polynomials was used to determine the polynomial expansion coef ficients. The results show good agreement with those obtained from finite d ifference computations in which the nonuniformity was approximated by a lar ge number of material regions.