Spherical harmonics -- finite element treatment of neutron transport in cylindrical geometry

A variational spherical harmonics (DPN ) method is used in conjunction with the finite element method to solve the transport of neutron beams. The method is developed for finite axisymmetric cylindrical geometry. In this model, the angular distribution along the path of neutron travel is separated into two sub-ranges of the forward and the backward moving particles. The system of the model equations is cast in terms of an even and an odd vector analogue to the even-parity transport technique. The finite element method is applied in space to solve the resulting coupled system of equations. A sourcefree cylinder with specified incident flux on the z = 0 surface is considered in this study. The model is based on the DPI and DP3 orders of expansion. The study demonstrates the advantages of the DPN method in accounting for the discontinuity of the angular flux in the direction of particles with no approximation. Results for the scalar flux are presented in isodose curve (contour) form for homogeneous and non-homogeneous media with different absorbing and purely scattering media. Numerical results compared favorably with those obtained by the exact solutions