Spherical Harmonics Method for a Two-Dimensional Multigroup Transport Equation Using a Semi-Discrete Ordinates Equation: Part I

It is shown that, after integrating the transport equation over the azimuthal angle of the polar coordinates, the resulting discrete ordinates equation with respect to the polar angle is equivalent to that of the spherical haromonics method provided that the discrete ordinates were chosen as the roots of the associated Legendre functions. The form of this semi-discrete ordinates equation is independent of the order of the approximation and simpler than those of the usual spherical harmonics method. The present method may be regarded as an extension of the Wick-Chandrasekhar method to multidimensional problems, since the present equation is reduced to the second-order form of the Wick-Chandrasekhar equation in the case of one-dimensional slab geometry.