Mixed-Hybrid Transport Discretization Using Even and Odd PN Expansions

A mixed-hybrid treatment of the spatial variables of the within-group neutron transport equation generalizes existing mixed and hybrid methods, combining their attractive features: the simultaneous approximation of even- and odd-parity angular flux components and the use of Lagrange multipliers to enforce interface continuity. A finite element spatial discretization and spherical harmonic angular expansions are used. We discuss rank conditions for the proposed methods and provide a new derivation of the Rumyantsev interface conditions. Even- and odd-parity interface continuity properties corresponding to these Rumyantsev conditions are established. We examine inclusion conditions and the interaction of the primal/dual distinction due to the spatial variable with the even/odd-order spherical harmonic approximation distinction due to the angular variable. Numerical solutions for both even- and odd-order spherical harmonic approximations are presented, and a promising enclosing property is observed in our results.