Results for the C5G7 benchmark problem using a subelement option of the variational nodal method

M. A. Smith; N. Tsoulfanidis; E. E. Lewis; G. Palmiotti; T. A. Taiwo

Results for the C5G7 benchmark problem using a subelement option of the variational nodal method

M. A. Smith^*, N. Tsoulfanidis, E. E. Lewis, G. Palmiotti, T. A. Taiwo

^*Corresponding author for this work

Mechanical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

Recently, an OECD benchmark problem was proposed to test the abilities of modern reactor physics codes to perform three-dimensional transport calculations without spatial homogenization of the fuel-coolant interfaces. To solve this benchmark problem we used the Argonne National Laboratory nodal transport code, VARIANT. VARIANT solves the even-parity transport equation on a nodal grid coupled with odd-parity Lagrange multipliers at the node interfaces. Each spatial node thus constitutes a primal hybrid finite element, with separate spatial approximations within the node and along the interface. The angular variables in the transport equation are treated with an expansion in either spherical harmonics or simplified spherical harmonics. To treat the spatial heterogeneities defined in the benchmark problem, we replaced the basis set of spatial polynomial trial functions used previously in VARIANT with a finite element spatial approximation. This approach subdivides the spatial node into finite elements with continuous, piecewise linear or quadratic trial functions; we refer to them as subelements. By allowing step changes in cross sections at the subelement interfaces, the spatial heterogeneities within the node can be treated explicitly. Using this new form of the VARIANT code we solved the two-dimensional and three-dimensional problems specified by the OECD benchmark and compared the results to reference multigroup Monte Carlo solutions.

Original language	English (US)
Title of host publication	Proceedings of the PHYSOR 2002 - International Conference on the New Frontiers of Nuclear Technology
Subtitle of host publication	Reactor Physics, Safety and High-Performance Computing - The ANS 2002 RPD Topical Meeting
Publisher	American Nuclear Society
ISBN (Electronic)	0894486721, 9780894486722
State	Published - 2002
Event	2002 International Conference on the New Frontiers of Nuclear Technology : Reactor Physics, Safety and High-Performance Computing, PHYSOR 2002 - Seoul, Korea, Republic of Duration: Oct 7 2002 → Oct 10 2002

Publication series

Name	Proceedings of the PHYSOR 2002 - International Conference on the New Frontiers of Nuclear Technology : Reactor Physics, Safety and High-Performance Computing - The ANS 2002 RPD Topical Meeting

Conference

Conference	2002 International Conference on the New Frontiers of Nuclear Technology : Reactor Physics, Safety and High-Performance Computing, PHYSOR 2002
Country/Territory	Korea, Republic of
City	Seoul
Period	10/7/02 → 10/10/02

Funding

This work is based, in part, on a dissertation submitted by the first author in partial fulfillment of the PhD requirements at the University of Missouri-Rolla. It was supported by the U.S. Department of Energy under Contract number W-31-109-ENG-38 and by the U.S. Department of Energy Contract number DE-FG07-98ID13632.

ASJC Scopus subject areas

Nuclear Energy and Engineering
Nuclear and High Energy Physics
Radiation
Safety, Risk, Reliability and Quality

Cite this

Smith, M. A., Tsoulfanidis, N., Lewis, E. E., Palmiotti, G., & Taiwo, T. A. (2002). Results for the C5G7 benchmark problem using a subelement option of the variational nodal method. In Proceedings of the PHYSOR 2002 - International Conference on the New Frontiers of Nuclear Technology: Reactor Physics, Safety and High-Performance Computing - The ANS 2002 RPD Topical Meeting (Proceedings of the PHYSOR 2002 - International Conference on the New Frontiers of Nuclear Technology : Reactor Physics, Safety and High-Performance Computing - The ANS 2002 RPD Topical Meeting). American Nuclear Society.

Smith, M. A. ; Tsoulfanidis, N. ; Lewis, E. E. et al. / Results for the C5G7 benchmark problem using a subelement option of the variational nodal method. Proceedings of the PHYSOR 2002 - International Conference on the New Frontiers of Nuclear Technology: Reactor Physics, Safety and High-Performance Computing - The ANS 2002 RPD Topical Meeting. American Nuclear Society, 2002. (Proceedings of the PHYSOR 2002 - International Conference on the New Frontiers of Nuclear Technology : Reactor Physics, Safety and High-Performance Computing - The ANS 2002 RPD Topical Meeting).

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title = "Results for the C5G7 benchmark problem using a subelement option of the variational nodal method",

abstract = "Recently, an OECD benchmark problem was proposed to test the abilities of modern reactor physics codes to perform three-dimensional transport calculations without spatial homogenization of the fuel-coolant interfaces. To solve this benchmark problem we used the Argonne National Laboratory nodal transport code, VARIANT. VARIANT solves the even-parity transport equation on a nodal grid coupled with odd-parity Lagrange multipliers at the node interfaces. Each spatial node thus constitutes a primal hybrid finite element, with separate spatial approximations within the node and along the interface. The angular variables in the transport equation are treated with an expansion in either spherical harmonics or simplified spherical harmonics. To treat the spatial heterogeneities defined in the benchmark problem, we replaced the basis set of spatial polynomial trial functions used previously in VARIANT with a finite element spatial approximation. This approach subdivides the spatial node into finite elements with continuous, piecewise linear or quadratic trial functions; we refer to them as subelements. By allowing step changes in cross sections at the subelement interfaces, the spatial heterogeneities within the node can be treated explicitly. Using this new form of the VARIANT code we solved the two-dimensional and three-dimensional problems specified by the OECD benchmark and compared the results to reference multigroup Monte Carlo solutions.",

author = "Smith, {M. A.} and N. Tsoulfanidis and Lewis, {E. E.} and G. Palmiotti and Taiwo, {T. A.}",

note = "Publisher Copyright: {\textcopyright} PHYSOR 2002.All right reserved.; 2002 International Conference on the New Frontiers of Nuclear Technology : Reactor Physics, Safety and High-Performance Computing, PHYSOR 2002 ; Conference date: 07-10-2002 Through 10-10-2002",

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Smith, MA, Tsoulfanidis, N, Lewis, EE, Palmiotti, G & Taiwo, TA 2002, Results for the C5G7 benchmark problem using a subelement option of the variational nodal method. in Proceedings of the PHYSOR 2002 - International Conference on the New Frontiers of Nuclear Technology: Reactor Physics, Safety and High-Performance Computing - The ANS 2002 RPD Topical Meeting. Proceedings of the PHYSOR 2002 - International Conference on the New Frontiers of Nuclear Technology : Reactor Physics, Safety and High-Performance Computing - The ANS 2002 RPD Topical Meeting, American Nuclear Society, 2002 International Conference on the New Frontiers of Nuclear Technology : Reactor Physics, Safety and High-Performance Computing, PHYSOR 2002, Seoul, Korea, Republic of, 10/7/02.

Results for the C5G7 benchmark problem using a subelement option of the variational nodal method. / Smith, M. A.; Tsoulfanidis, N.; Lewis, E. E. et al.
Proceedings of the PHYSOR 2002 - International Conference on the New Frontiers of Nuclear Technology: Reactor Physics, Safety and High-Performance Computing - The ANS 2002 RPD Topical Meeting. American Nuclear Society, 2002. (Proceedings of the PHYSOR 2002 - International Conference on the New Frontiers of Nuclear Technology : Reactor Physics, Safety and High-Performance Computing - The ANS 2002 RPD Topical Meeting).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Tsoulfanidis, N.

AU - Lewis, E. E.

AU - Palmiotti, G.

AU - Taiwo, T. A.

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N2 - Recently, an OECD benchmark problem was proposed to test the abilities of modern reactor physics codes to perform three-dimensional transport calculations without spatial homogenization of the fuel-coolant interfaces. To solve this benchmark problem we used the Argonne National Laboratory nodal transport code, VARIANT. VARIANT solves the even-parity transport equation on a nodal grid coupled with odd-parity Lagrange multipliers at the node interfaces. Each spatial node thus constitutes a primal hybrid finite element, with separate spatial approximations within the node and along the interface. The angular variables in the transport equation are treated with an expansion in either spherical harmonics or simplified spherical harmonics. To treat the spatial heterogeneities defined in the benchmark problem, we replaced the basis set of spatial polynomial trial functions used previously in VARIANT with a finite element spatial approximation. This approach subdivides the spatial node into finite elements with continuous, piecewise linear or quadratic trial functions; we refer to them as subelements. By allowing step changes in cross sections at the subelement interfaces, the spatial heterogeneities within the node can be treated explicitly. Using this new form of the VARIANT code we solved the two-dimensional and three-dimensional problems specified by the OECD benchmark and compared the results to reference multigroup Monte Carlo solutions.

AB - Recently, an OECD benchmark problem was proposed to test the abilities of modern reactor physics codes to perform three-dimensional transport calculations without spatial homogenization of the fuel-coolant interfaces. To solve this benchmark problem we used the Argonne National Laboratory nodal transport code, VARIANT. VARIANT solves the even-parity transport equation on a nodal grid coupled with odd-parity Lagrange multipliers at the node interfaces. Each spatial node thus constitutes a primal hybrid finite element, with separate spatial approximations within the node and along the interface. The angular variables in the transport equation are treated with an expansion in either spherical harmonics or simplified spherical harmonics. To treat the spatial heterogeneities defined in the benchmark problem, we replaced the basis set of spatial polynomial trial functions used previously in VARIANT with a finite element spatial approximation. This approach subdivides the spatial node into finite elements with continuous, piecewise linear or quadratic trial functions; we refer to them as subelements. By allowing step changes in cross sections at the subelement interfaces, the spatial heterogeneities within the node can be treated explicitly. Using this new form of the VARIANT code we solved the two-dimensional and three-dimensional problems specified by the OECD benchmark and compared the results to reference multigroup Monte Carlo solutions.

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M3 - Conference contribution

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T3 - Proceedings of the PHYSOR 2002 - International Conference on the New Frontiers of Nuclear Technology : Reactor Physics, Safety and High-Performance Computing - The ANS 2002 RPD Topical Meeting

BT - Proceedings of the PHYSOR 2002 - International Conference on the New Frontiers of Nuclear Technology

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Smith MA, Tsoulfanidis N, Lewis EE, Palmiotti G, Taiwo TA. Results for the C5G7 benchmark problem using a subelement option of the variational nodal method. In Proceedings of the PHYSOR 2002 - International Conference on the New Frontiers of Nuclear Technology: Reactor Physics, Safety and High-Performance Computing - The ANS 2002 RPD Topical Meeting. American Nuclear Society. 2002. (Proceedings of the PHYSOR 2002 - International Conference on the New Frontiers of Nuclear Technology : Reactor Physics, Safety and High-Performance Computing - The ANS 2002 RPD Topical Meeting).

Results for the C5G7 benchmark problem using a subelement option of the variational nodal method

Abstract

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Funding

ASJC Scopus subject areas

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