Development of a modular nodal method for solving three dimensional spherical harmonic equations

A nodal method based upon the least squares minimization technique. has been developed for solving the neutron transport equation using spherical harmonics approximation in 3-dimensional Cartesian coordinates. The second order form of the spherical harmonic differential equations based upon the even parity form of the transport equation are utilized. The governing equations are casted into a set of elliptic type differential equations for which the coefficients can be generated for any spherical harmonics approximation order automatically. The coeffICients of the mixed type boundary conditiions are obtained through recurrence relationships for any order as well. The approximation order to be used in the nodes can vary according to the physics of the problem and determined by the computer code.