The solution of the neutron diffusion equation by the hierarchical expansion method

A modal method for the numerical solution of the two-dimensional two-group neutron diffusion equation in rectangular geometry is presented. The method is based on the expansion of the group neutron fluxes by hierarchical functions. The weighted residual procedure is used to obtain the solution equations. The expansion functions are Legendre polynomials adjusted in the rectangular nodes in a novel form, so that corner, side and surface functions are distinguished. The order of the approximation for the side and surface expansion are up to desired or necessary degree. This formalism has been programmed in a computer code called HEMDOC. The two-dimensional IAEA benchmark problem was tested, showing the capability of the method to yield accurate numerical solutions on coarse spatial grids. (author)