Discrete ordinates with new quadrature sets and modified source conditions

Conference · Sun Jan 01 04:00:00 EST 1989 · Transactions of the American Nuclear Society; (USA)

OSTI ID:6504889

Ganguly, K

A major shortcoming of the discrete ordinates method with the Gauss-Legendre quadrature set is that when the number of secondaries per primary c and the order of approximation N are not too large, all the (N + 1)v (the flux being of the form exp({minus}x/v)) lie in ({minus}1,1). It is known, however, that the largest v{sub j} corresponding to the asymptotic flux is greater than unity. The Legendre polynomial used for obtaining the quadrature set is orthogonal with respect to weight unity in the range ({minus}1,1). However, the Case and Zweifel eigenfunctions derived from the exact solution of one-speed transport theory are orthogonal with respect to a complicated weight function w({mu}) and {mu} in the half-range and full-range cases, respectively. In this paper, the authors have used a set of orthogonal polynomials with respect to w ({mu}) to develop quadrature sets to be used in the discrete ordinates calculation.

• OSTI ID: 6504889
• Report Number(s): CONF-891103--
• Conference Information: Journal Name: Transactions of the American Nuclear Society; (USA) Journal Volume: 60
• Country of Publication: United States
• Language: English

Related Subjects

654003* -- Radiation & Shielding Physics-- Neutron Interactions with Matter
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ACCURACY
DISCRETE ORDINATE METHOD
EIGENFUNCTIONS
FUNCTIONS
GAUSS FUNCTION
LEGENDRE POLYNOMIALS
NEUTRON TRANSPORT THEORY
ORTHOGONAL TRANSFORMATIONS
POLYNOMIALS
QUADRATURES
TRANSFORMATIONS
TRANSPORT THEORY