Comparison of simplified and standard spherical harmonics in the variational nodal method

摘要

Recently, the variational nodal method has been extended through the use of the Rumyantsev interface conditions to solve the spherical harmonics (P(sub N)) equations of arbitrary odd order. In this paper, the authors generalize earlier x-y geometry work to fit the corresponding simplified spherical harmonics (SP(sub N)) equations into the variational nodal framework. Both P(sub N) and SP(sub N) approximations are implemented in the multigroup VARIANT code at Argonne National Laboratory in two and three dimensional Cartesian and hexagonal geometries. The availability of angular approximations through P(sub 5) and SP(sub 5), and of flat, linear and quadratic spatial interface approximations allows investigation of both spatial truncation and angular approximation errors. Moreover, the SP(sub 3) approximation offers a cost-effective method for reducing transport errors.