A coarse-mesh numerical method for one-speed neutron transport eigenvalue problems in two-dimensional Cartesian geometry Original Research Article

We describe a hybrid spectral nodal method applied to one-speed SN eigenvalue problems in x,y-geometry for nuclear reactor global calculations. To solve the transverse-integrated SN nodal equations, we generalize the spectral diamond (SD) method, that we developed for numerically solving slab-geometry SN eigenvalue problems with no spatial truncation error. In the present generalization, we approximate the transverse leakage through the edges of each spatial node by constants, so we call our method the SD-constant nodal (SD-CN) method that we use in the fuel regions of the nuclear reactor core. In the non-multiplying regions, e.g., reflector and baffle, we use the spectral Greenʹs function-constant nodal (SGF-CN) method; hence the hybrid characteristic of our method. In order to converge the numerical solution for each SN “fixed source” problem (inner iterations) in each outer iteration (power method), we use the one-node block inversion (NBI) scheme. We show some numerical results to a typical model problem to illustrate the methodʹs accuracy in coarse-mesh calculations.