THE SPHERICAL-HARMONICS METHOD FOR THE MULTIGROUP TRANSPORT-EQUATION IN X-Y GEOMETRY

A spherical harmonics equation in the form of a second-order differential equation is derived for the 2-D x-y geometry, including higher-order scattering within a group. Using this equation, a multigroup transport code for the spherical harmonics method of a general order of approximation is developed. Some numerical examples, including typical problems for the ray effect, are presented and compared with those obtained by the discrete-ordinates method. It is shown that the present method gives more accurate results than the discrete-ordinates method, although this spherical harmonics code requires more computer memory than the discrete-ordinates code.