Simplified spherical harmonics in the variational nodal method

The multigroup simplified spherical harmonics equations with anisotropic scattering are derived from a variational principle that preserves nodal balance. The resulting equations are discretized using a Ritz procedure with spatial trial functions that are complete polynomials within the nodes and on the interfaces. The resulting equations are cast in a response matrix form and incorporated as an option of the variational nodal spherical harmonics code VARIANT. Fixed source and multigroup eigenvalue calculations are performed on benchmark problems. The accuracy and computational efficiency of spherical harmonic and simplified spherical harmonic approximations are compared, and the compensating effects of spatial and angular truncation errors are examined. The results indicate that in most situations, simplified and standard spherical harmonics results of the same order are in close agreement, while the use of simplified spherical harmonics substantially reduces computing costs.