An extended half-range spherical harmonics method for first-order neutron transport equation based on variational treatment

A new variational approach with anisotropic scattering kernel for first order neutron transport equation based on Finite Element Method (FEM) and Double-PN (DPN) approximation has been introduced. In presented variational principle, the angular dependence of the neutron flux has been separated into two sub-ranges of the forward and backward moving particles. The applied boundary conditions for the DPN method are straightforward in comparison to the conditions for the PN method. The method has also been extended for 2D plane geometry by using extended half-range spherical harmonics method. By defining a new variational principle, the discontinuity of angular flux on the boundary surface has been treated. A new computing program has been developed, to calculate the angular flux by this method which has the capability to solve neutron transport equation by arbitrary DPN approximation in 1D anisotropic scattering media. Moreover, by investigating extended half-range spherical harmonics method, the program has been developed for 2D geometry. The efficacy of the method is assessed by comparing the required order of angular expansion which is necessary to achieve fine results in several benchmarks. The results demonstrate the superiority of the method against traditional PN method.