Accurate reflective boundary condition in the PN method

Accurate implementation of reflective Boundary Condition (B.C.) in the PN method for both forward and adjoint analysis in one, two and three dimensional geometries is investigated in detail. Slab, spherical and cylindrical geometries are covered for 1D space, while a comprehensive procedure for general 3D Cartesian geometry is explained which encapsulates 2D (XY) geometry as a special case. It is shown that the reflective B.C. in the PN method ends to a series of moment couplings on the mirror surface which should be treated as an essential B.C. While these constraints are derived for the conventional PN method, they are applicable for the even parity PN approach, as well. Necessary guideline for imposing reflective constraints on the final system of linear equations in eigenvalue search or fixed source problems is also described. We finally verify the proposed approach by several test cases at the end.