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}
}