Second-order discrete ordinate P/sub L/ equations in multi-dimensional geometry

Journal Article · Wed Aug 01 04:00:00 EDT 1973 · J. Nucl. Energy, v. 27, no. 8, pp. 577-590

OSTI ID:4358687

Jung, J; Ohtani, N; Kobayashi, K; Nishihara, H

Discrete ordinate neutron transport equati ons which are equivalert to the P/sub L/ approximati on are derived in order to eliminate the current problem in the numerical solutions for the transport equation. The number of the unknowns which remain to be solved in the discrete ordinate equations is consistent with that of the independent basic functions appearing in the P/sub L/ solution. For even P/sub L/ approximati on in one-dimensional slab geometry, a system of equations which are satisfied by the L unknowns is derived by eliminating the L-th Legendre moment. For multi -dimensional geometry, discrete ordinate equations of the second order which are equivalent to the P/sub L/ approximation are proposed by following Davis' method for the derivation of the even-parity second-order form of the odd P/sub L/ equations. In this case, the total number of the quadrature points is just equal to that of the independent basic functions. Finally, the boundary conditions of the P/sub L/ approximati on in x--y geometry are transformed into those for the corresponding discrete ordinate equations. As for the boundary conditions, material interface, reflecti ng and vacuum boundary conditions are considered. (auth)

• Research Organization: Kyoto Univ.
• NSA Number: NSA-29-017117
• OSTI ID: 4358687
• Journal Information: J. Nucl. Energy, v. 27, no. 8, pp. 577-590, Journal Name: J. Nucl. Energy, v. 27, no. 8, pp. 577-590; ISSN JNUCA
• Country of Publication: United Kingdom
• Language: English

Related Subjects

*NEUTRON DIFFUSION EQUATION-- NUMERICAL SOLUTION
*NEUTRON TRANSPORT THEORY-- DISCRETE ORDINATE METHOD
*SLABS-- NEUTRON TRANSPORT
BOUNDARY CONDITIONS
LEGENDRE POLYNOMIALS
N68100* --Physics (Nuclear)--Neutron Interactions with Matter
NEUTRONS
SPHERICAL HARMONICS METHOD
TWO- DIMENSIONAL CALCULATIONS