Numerical Solutions of Discrete-Ordinate Neutron Transport Equations Equivalent to P_L Approximation in X-Y Geometry

Abstract

A numerical method for solving the steady-state one-velocity neutron transport equation in x-y geometry is presented. It is based on the concept of combining the spherical harmonics theory with the discrete-ordinate method. The validity of the method is illustrated by several numerical computations using the TWOTRAN-PLXY code, formulated by modifying the ordinary discrete-ordinate code TWOTRAN-(x, y).
Through numerical studies, it is shown that the present method is effective for obtaining solutions of high accuracy, as well as for eliminating the ray effects present in the ordinary discrete-ordinate method. As for the techniques for accelerating the convergence of the iterative solutions, it is proved that the Chebyshev device works well for the present method while whole-system rebalancing is found to be less effective.