skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Improvement of variational nodal transport methods by Lagrange multiplier techniques

Abstract

It has been demonstrated in earlier work that nodal transport methods can be formulated through the use of a variational form of the even-parity transport equation. The resulting methods have been used to obtain coarse-mesh solutions to two-dimensional P/sub 1/ and P/sub 3/ equations in a response matrix form. The formalism preserves neutron balance in each spatial node, while allowing the flux distribution within a node to be treated as a complete polynomial or other finite element like trial function. Subsequently, the method has been formulated as a global functional in which the odd-parity interface conditions appear as Lagrange multipliers. It is shown that the Lagrange multiplier formulation may be used to reduce the number of basis functions used to specify the interface conditions, thereby reducing the dimension of the nodal response matrices without a commensurate loss of accuracy. Specifically, by careful choice of Lagrange multiplier trial functions, one can cut the number of interface conditions by two and still obtain near P/sub 3/ accuracy. Moreover, the resulting formalism suffers neither from ray effects nor from the inaccuracies for streaming diagonal to the coordinate directions that have been observed in some nodal transport methods.

Authors:
Publication Date:
Research Org.:
Argonne National Lab., IL (USA)
OSTI Identifier:
6892937
Report Number(s):
CONF-8711195-
Journal ID: CODEN: TANSA; TRN: 88-033057
Resource Type:
Conference
Journal Name:
Trans. Am. Nucl. Soc.; (United States)
Additional Journal Information:
Journal Volume: 55; Conference: American Nuclear Society winter meeting, Los Angeles, CA, USA, 15 Nov 1987
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; NEUTRON TRANSPORT; LAGRANGE EQUATIONS; TWO-DIMENSIONAL CALCULATIONS; ACCURACY; FINITE ELEMENT METHOD; NEUTRON FLUX; DIFFERENTIAL EQUATIONS; EQUATIONS; NEUTRAL-PARTICLE TRANSPORT; NUMERICAL SOLUTION; PARTIAL DIFFERENTIAL EQUATIONS; RADIATION FLUX; RADIATION TRANSPORT; 654003* - Radiation & Shielding Physics- Neutron Interactions with Matter

Citation Formats

Lewis, E E. Improvement of variational nodal transport methods by Lagrange multiplier techniques. United States: N. p., 1987. Web.
Lewis, E E. Improvement of variational nodal transport methods by Lagrange multiplier techniques. United States.
Lewis, E E. 1987. "Improvement of variational nodal transport methods by Lagrange multiplier techniques". United States.
@article{osti_6892937,
title = {Improvement of variational nodal transport methods by Lagrange multiplier techniques},
author = {Lewis, E E},
abstractNote = {It has been demonstrated in earlier work that nodal transport methods can be formulated through the use of a variational form of the even-parity transport equation. The resulting methods have been used to obtain coarse-mesh solutions to two-dimensional P/sub 1/ and P/sub 3/ equations in a response matrix form. The formalism preserves neutron balance in each spatial node, while allowing the flux distribution within a node to be treated as a complete polynomial or other finite element like trial function. Subsequently, the method has been formulated as a global functional in which the odd-parity interface conditions appear as Lagrange multipliers. It is shown that the Lagrange multiplier formulation may be used to reduce the number of basis functions used to specify the interface conditions, thereby reducing the dimension of the nodal response matrices without a commensurate loss of accuracy. Specifically, by careful choice of Lagrange multiplier trial functions, one can cut the number of interface conditions by two and still obtain near P/sub 3/ accuracy. Moreover, the resulting formalism suffers neither from ray effects nor from the inaccuracies for streaming diagonal to the coordinate directions that have been observed in some nodal transport methods.},
doi = {},
url = {https://www.osti.gov/biblio/6892937}, journal = {Trans. Am. Nucl. Soc.; (United States)},
number = ,
volume = 55,
place = {United States},
year = {Thu Jan 01 00:00:00 EST 1987},
month = {Thu Jan 01 00:00:00 EST 1987}
}

Conference:
Other availability
Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that hold this conference proceeding.

Save / Share: