The solution of the multigroup neutron transport equation using spherical harmonics

Journal Article · Sun May 01 04:00:00 EDT 1983 · Nucl. Sci. Eng.; (United States)

OSTI ID:5502121

Fletcher, J K

A solution of the multigroup neutron transport equation in one, two, or three space dimensions is presented. The flux /phi/ /SUB g/ (r,..cap omega..) at point r in direction ..cap omega.. for energy group g takes the form of an expansion in unnormalized spherical harmonics whose solution takes into account the axial and azimuthal angles of ..cap omega.., the associated Legendre polynomials, and an arbitrary odd number. Using various recurrence formulas, a linked set of first-order differential equations results. Terms with odd limits are eliminated yielding a second-order system to be solved by two methods. First, a finite difference formulation using an iterative procedure is given, and second, in XYZ and XY geometry, a finite element solution is presented. Results for a test problem using both methods are exhibited and compared.

• Research Organization: United Kingdom Atomic Energy Authority Risley, Warrington, Cheshire
• OSTI ID: 5502121
• Journal Information: Nucl. Sci. Eng.; (United States), Journal Name: Nucl. Sci. Eng.; (United States) Vol. 84:1; 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
FINITE DIFFERENCE METHOD
FINITE ELEMENT METHOD
FUNCTIONS
HARMONICS
ITERATIVE METHODS
LEGENDRE POLYNOMIALS
MULTIGROUP THEORY
NEUTRON FLUX
NEUTRON TRANSPORT THEORY
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
OSCILLATIONS
POLYNOMIALS
RADIATION FLUX
THREE-DIMENSIONAL CALCULATIONS
TRANSPORT THEORY
TWO-DIMENSIONAL CALCULATIONS