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Title: Spherical quadratures for the discrete ordinates method.

Abstract

No abstract prepared.

Authors:
; ; ; ; ;
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
NE
OSTI Identifier:
927291
Report Number(s):
ANL/NE/CP-58414
TRN: US0803153
DOE Contract Number:
DE-AC02-06CH11357
Resource Type:
Conference
Resource Relation:
Journal Name: Trans. Am. Nucl. Soc.; Journal Volume: 96; Journal Issue: 04/2007; Conference: 2007 ANS Annual Meeting; Jun 24-28, 2007; Boston, MA
Country of Publication:
United States
Language:
ENGLISH
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; DISCRETE ORDINATE METHOD; QUADRATURES; RADIATION TRANSPORT

Citation Formats

Rabiti, C., Wolters, E., Smith, M.A., Palmiotti, G., Nuclear Engineering Division, and Univ. of Michigan. Spherical quadratures for the discrete ordinates method.. United States: N. p., 2007. Web.
Rabiti, C., Wolters, E., Smith, M.A., Palmiotti, G., Nuclear Engineering Division, & Univ. of Michigan. Spherical quadratures for the discrete ordinates method.. United States.
Rabiti, C., Wolters, E., Smith, M.A., Palmiotti, G., Nuclear Engineering Division, and Univ. of Michigan. Sun . "Spherical quadratures for the discrete ordinates method.". United States. doi:.
@article{osti_927291,
title = {Spherical quadratures for the discrete ordinates method.},
author = {Rabiti, C. and Wolters, E. and Smith, M.A. and Palmiotti, G. and Nuclear Engineering Division and Univ. of Michigan},
abstractNote = {No abstract prepared.},
doi = {},
journal = {Trans. Am. Nucl. Soc.},
number = 04/2007,
volume = 96,
place = {United States},
year = {Sun Apr 01 00:00:00 EDT 2007},
month = {Sun Apr 01 00:00:00 EDT 2007}
}

Conference:
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  • Abstract not provided.
  • It is shown that the semi-discrete ordinates equation can be used to create a computer program for a general order of P/sub L/ approximations for solving the multigroup neutron transport equation in two-dimensional x-y geometry. Sample calculations for problems using up to a P/sub 7/ approximation and up to four energy groups are given, and the results are compared with corresponding ones obtained by the discrete ordinates method. As the order of approximations increases, both results show good agreement, when the influence of the ray effect is not appreciable. The advantage of the present method is that the ray effectmore » does not occur, which is the problem in the discrete ordinates method.« less
  • It is shown that, after integrating the transport equation over the azimuthal angle of the polar coordinates, the resulting discrete ordinates equation with respect to the polar angle is equivalent to that of the spherical haromonics method provided that the discrete ordinates were chosen as the roots of the associated Legendre functions. The form of this semi-discrete ordinates equation is independent of the order of the approximation and simpler than those of the usual spherical harmonics method. The present method may be regarded as an extension of the Wick-Chandrasekhar method to multidimensional problems, since the present equation is reduced tomore » the second-order form of the Wick-Chandrasekhar equation in the case of one-dimensional slab geometry.« less
  • The authors extend the method of simplified discrete ordinates (SS{sub N}) to spherical geometry. The motivation for such an extension is that the appearance of the angular derivative (redistribution) term in the spherical geometry transport equation makes it difficult to decide which differencing scheme best approximates this term. In the present method, the angular derivative term is treated implicitly and thus avoids the need for the approximation of such term. This method can be considered to be analytic in nature with the advantage of being free from spatial truncation errors from which most of the existing transport codes suffer. Inmore » addition, it treats the angular redistribution term implicitly with the advantage of avoiding approximations to that term. The method also can handle scattering in a very general manner with the advantage of spending almost the same computational effort for all scattering modes. Moreover, the methods can easily be applied to higher-order S{sub N} calculations.« less