Richardson extrapolation applied to difference methods for numerically solving the neutron transport equation in spherical geometry

Journal Article · Mon Jul 01 04:00:00 EDT 1991 · Nuclear Science and Engineering; (United States)

OSTI ID:5611965

Abbott, W E ^[1]; Allen, E J ^[2]

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1. Radian Corp., Austin, TX (United States)
2. Texas Tech Univ., Lubbock, TX (United States). Dept. of Mathematics

In this paper two difference schemes are derived for numerically solving the transport equation in spherical geometry. The first difference method is positive; i.e., the calculated fluxes are never negative. furthermore, for the first method, the error expansion is suitable for applying Richardson extrapolation with respect to both spatial and angular variables to increase the accuracy of the approximate fluxes. Numerical experiments illustrate the accuracy obtained using the procedure, as well as demonstrate that the accuracy of the second difference method is significantly improved through application of Richardson extrapolation. In addition, the numerical results indicate that the second method is significantly more accurate than the standard nonextrapolated diamond-difference method for numerically solving the transport equation in spherical geometry.

• OSTI ID: 5611965
• Journal Information: Nuclear Science and Engineering; (United States), Journal Name: Nuclear Science and Engineering; (United States) Vol. 108:3; ISSN 0029-5639; ISSN NSENA
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
220100 -- Nuclear Reactor Technology-- Theory & Calculation
663610* -- Neutron Physics-- (1992-)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ADJOINT DIFFERENCE METHOD
EQUATIONS
EXTRAPOLATION
KINETICS
MATHEMATICAL MODELS
NEUTRON FLUX
NEUTRON TRANSPORT THEORY
NUCLEAR MODELS
NUMERICAL SOLUTION
RADIATION FLUX
REACTOR KINETICS
RICHARDSON EQUATION
SPHERICAL MODEL
TRANSPORT THEORY