The Multi-PN approximation to neutron transport equation

The Multi-PN (MPN) approximation to the first-order neutron transport equation in one- and two-dimensional geometries is presented using a variational approach. The directional variations of the angular flux have been modeled by separate spherical harmonics expansions in M subdomains, while finite elements have been utilized to represent the spatial dependence. A straightforward procedure has been proposed to handle any order of discretized polynomial expansions in both isotropic and anisotropic scattering medium. A key problem with much of the literature regarding the full-range spherical harmonic method is that it cannot exactly describe the discontinuous nature of the angular flux. Thus, the use of customary expansions leads to substantial defect at boundary and interface of two distinct media (e.g. interface of fuel elements and moderators). The major contribution of the MPN discretization is a theory that overcomes these difficulties. The work represents the generalization of the Double-PN (DPN) approximation previously applied to the neutron transport equation. Numerical results in one- and two-dimensional problems compare MPN and customary PN calculations to the reference transport calculations.