Second-order discrete ordinate P/sub L/ equations in multi-dimensional geometry
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, Other Information: Orig. Receipt Date: 30-JUN-74; Bib. Info. Source: UK (United Kingdom (sent to DOE from))
- Country of Publication:
- United Kingdom
- Language:
- English
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