Polynomial nodal method for solving neutron diffusion equations in hexagonal-z geometry

A polynomial nodal method is developed to solve few-group neutron diffusion equations in hexagonal-z geometry. The method is based on conformal mapping of a hexagon into a rectangle. The resulting equations are solved using a fourth-order expansion of the transverse-integrated neutron flux into orthogonal polynomials. The transverse leakage is represented using constant neutron currents at the faces of the internal reactor nodes and a linear approximation of the current at the faces of the nodes at the reactor boundary. A nonlinear iteration procedure is used for solving the nodal equations. The neutron flux expansion coefficients are found by considering a two-node problem for each node interface. Due to orthogonality of the polynomials, 8G nodal equations for the two-node problem are reduced to two systems of G and 2G equations. The method is implemented into the nodal neutron kinetics code SKETCH-N. The results of steady-state benchmark problems have demonstrated excellent accuracy of the method.