The discrete-ordinate method in diffusive regimes

Journal Article · Tue Jan 01 04:00:00 EST 1991 · Transport Theory and Statistical Physics; (United States)

DOI:https://doi.org/10.1080/00411459108203913· OSTI ID:7234598

Jin, Shi; Levermore, D ^[1]

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1. Univ. of Arizona, Tucson (United States)

In highly scattering regimes, the transport equations has a limit in which the leading behavior of its solution is determined by the solution of a diffusion equation. A boundary layer with a thickness of a few mean free paths usually forms between the domain boundary and the interior region, through which the given transport boundary conditions are matched to the interior tablesolution by properly choosing the boundary conditions for the diffusion equation. In order for a numerical scheme to be effective in these regimes, it must have both a correct interior diffusion limit and a correct boundary condition limit. The behavior of the discrete-ordinate method is studied in these limits and formulas for the resulting diffusion equation and its boundary conditions are found. By imposing the condition that these limiting formulas be the same as those for the transport equation, a new constraint on the quadrature set is obtained and a way to discretize the boundary data based on the discrete W-function is suggested. Numerical examples for isotropic materials demonstrate the theoretic results.

• OSTI ID: 7234598
• Journal Information: Transport Theory and Statistical Physics; (United States), Journal Name: Transport Theory and Statistical Physics; (United States) Vol. 20:5-6; ISSN TTSPB; ISSN 0041-1450
• Country of Publication: United States
• Language: English

Related Subjects

663610* -- Neutron Physics-- (1992-)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BOUNDARY LAYERS
DIFFUSION
DISCRETE ORDINATE METHOD
ISOTROPY
LAYERS
MEAN FREE PATH
NEUTRON TRANSPORT THEORY
NUMERICAL SOLUTION
QUADRATURES
TRANSPORT THEORY