Hybrid Methods in Engineering

A HYBRID SPECTRAL NODAL METHOD FOR ONE-SPEED DISCRETE ORDINATES EIGENVALUE PROBLEMS IN TWO-DIMENSIONAL CARTESIAN GEOMETRY

ABSTRACT

We describe a hybrid spectral nodal method applied to one-speed S_N eigenvalue problems in X, Y-geometry for nuclear reactor global calculations. To solve the transverse-integrated S_N nodal equations, we generalize the spectral diamond (SD) method that we developed for numerically solving slab-geometry S_N 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, which we use in the fuel regions of the nuclear reactor core. In the nonmultiplying regions, for example, reflector and baffle, we use the spectral Green's function-constant nodal (SGF-CN) method; hence the hybrid characteristic of our method. To converge the numerical solution for each S_N fixed source problem (inner iterations) in each outer iteration (power method), we use the one-node block inversion (NBI) scheme. We show numerical results for two typical model problems to illustrate the method's accuracy in coarse-mesh calculations and to justify the hybrid characteristic of the numerical algorithm.