Compatible product angular quadrature for neutron transport in x-y geometry

Journal Article · Sat Oct 01 04:00:00 EDT 1977 · Nucl. Sci. Eng.; (United States)

OSTI ID:5295864

Abu-Shumays, I K

The main features of this paper are the utilization of inherent two-dimensional symmetries and the development of accurate angular quadrature coordinates and weights especially suited for the net and/or partial currents and all the net and/or partial moments of the neutron flux up to a given order. Three classes of true analogs of the one-dimensional single-Gauss and double-Gauss are considered for two-dimensional x-y problems with rectangular spatial mesh subdivisions. The first is single-range quadrature, most suitable for the asymptotic regions where the vector flux of neutrons can be well approximated by polynomials in ..cap omega../sub x/ and ..cap omega../sub y/ defined over the entire unit sphere of angular directions ..cap omega... This quadrature can be used whenever distances between material interfaces are large with respect to the neutron mean-free-path (mfp). The second is double-range quadrature, most suitable at material interfaces where the unit sphere can be split into two hemispheres, one in each material region, and the vector flux can be well approximated by two possibly distinct polynomials in ..cap omega../sub x/ and ..cap omega../sub y/, one in each hemisphere. This quadrature can be used whenever material interfaces and currents are important along either the x or the y direction but not both. The third is quadruple-range quadrature, most suitable at corners where the unit sphere can be split into four quadrants and the vector flux can be well approximated by four possibly distinct polynomials in ..cap omega../sub x/ and ..cap omega../sub y/, one in each quadrant. This quadrature explicitly allows for discontinuities at corners and is appropriate for highly heterogeneous problems where distances between material corners are small with respect to the mfp. For simplicity, only product formulas are considered, where the angular integrals are split into separate integrals over polar and azimuthal directions.

• Research Organization: Bettis Atomic Power Lab., West Mifflin, PA
• OSTI ID: 5295864
• Journal Information: Nucl. Sci. Eng.; (United States), Journal Name: Nucl. Sci. Eng.; (United States) Vol. 64:2; ISSN NSENA
• Country of Publication: United States
• Language: English

Related Subjects

654003* -- Radiation & Shielding Physics-- Neutron Interactions with Matter
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
EIGENVALUES
MATHEMATICS
NEUTRON FLUX
NEUTRON TRANSPORT THEORY
NUMERICAL ANALYSIS
QUADRATURES
RADIATION FLUX
TRANSPORT THEORY