Singular perturbation solutions of the neutron transport equation

Journal Article · Wed May 01 04:00:00 EDT 1996 · Nuclear Science and Engineering

OSTI ID:264353

Losey, D C ^[1]; Lee, J C; Martin, W R; Adamson, Jr, T C ^[2]

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1. Westinghouse Savannah River Co., Aiken, SC (United States)
2. Univ. of Michigan, Ann Arbor, MI (United States)

A singular perturbation technique is applied to the time-independent one-dimensional neutron transport equation with isotropic neutron scattering. The technique reduces the transport problem to a series of diffusion theory problems in the interior medium and a series of simplified transport problems solved analytically in the boundary layer. The analysis provides a consistent method for deriving and comparing various diffusion theory approximations to the transport equation. In addition, the resulting scheme provides a systematic method for enhancing the accuracy of diffusion theory calculations of global flux distributions. A general asymptotic expansion of c, the number of secondary neutrons per collision, is obtained and an O({epsilon}{sup 2}) correction to the diffusion theory boundary condition at a material interface is derived. The perturbation technique has been applied analytically to both fixed source and criticality problems. The technique is also incorporated in a multigroup diffusion theory computer code. In test calculations, the error in flux distributions is reduced to about one-half that achieved with standard diffusion theory techniques.

• DOE Contract Number: AC09-89SR18035
• OSTI ID: 264353
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 1 Vol. 123; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ANALYTICAL SOLUTION
MULTIGROUP THEORY
NEUTRON DIFFUSION EQUATION
NEUTRON FLUX
NEUTRON TRANSPORT THEORY
PERTURBATION THEORY