S{sub N} Schemes, Linear Infinite-Medium Solutions, and the Diffusion Approximation
It is standard practice to require an S{sub N} spatial discretization scheme to preserve the ''flat infinite-medium'' solution of the transport equation. This solution consists of a spatially independent source that gives rise to a spatially independent flux. However, there exist many other exact solutions of the transport equation that are typically not preserved by approximation schemes. Here, we discuss one of these: a source that is linear in space giving rise to an angular flux that is linear in space and angle. For one-group, planar-geometry S{sub N} problems, we show that (a) among the class of weighted-diamond schemes, only one - the diamond-difference scheme - preserves this exact ''linear'' solution; (b) consequently, only the diamond scheme preserves the correct Fick's Law; and (c) as a further consequence, nondiamond schemes can produce significant errors (not observed in the diamond solution) for diffusive problems with spatial cells that are not optically thin. These results demonstrate that it is advantageous for S{sub N} discretization schemes to preserve the ''flat'' and ''linear'' infinite-medium solutions.
- Research Organization:
- University of Michigan, Ann Arbor, MI (US)
- Sponsoring Organization:
- None (US)
- OSTI ID:
- 785127
- Report Number(s):
- ISSN-0003-018X; CODEN TANSAO; ISSN-0003-018X; CODEN TANSAO; TRN: US0108373
- Resource Relation:
- Conference: 2001 Annual Meeting, Milwaukee, WI (US), 06/17/2001--06/21/2001; Other Information: Transactions of the American Nuclear Society, volume 84; PBD: 17 Jun 2001
- Country of Publication:
- United States
- Language:
- English
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