Accurate reflective boundary condition in the PN method. (November 2017)

• Record Type: Journal Article
• Authors: Yousefi, Mostafa; Zolfaghari, A.; Minuchehr, A.; Abbassi, M.R.
• Is Part Of: Annals of nuclear energy. Volume 109(2017:Nov.)
• Page Start: 583
• Page End: 599
• Publication Date: 2017-11
• Subjects: Reflective boundary condition -- PN method -- Spherical harmonics expansion -- Neutron transport -- Radiation transport; Nuclear energy -- Periodicals; Nuclear engineering -- Periodicals; 621.4805
• DOI: 10.1016/j.anucene.2017.05.057
• Languages: English
• ISSNs: 0306-4549

Abstract

Highlights: Accurate reflective boundary condition in 1D, 2D and 3D geometry is described in details. Necessary moments coupling are derived for arbitrary oriented reflective surfaces in 3D geometry. Reflective BC for curvilinear geometries is also explained with sufficient details. Mandatory manipulations in global matrix and source vector are derived and discussed. Method is applicable for all PN -based (forward and adjoint) approaches including even parity ones. Abstract: 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.