A first-order spherical harmonics formulation compatible with the variational nodal method

M. A. Smith; E. E. Lewis; G. Palmiotti; W. S. Yang

A first-order spherical harmonics formulation compatible with the variational nodal method

M. A. Smith, E. E. Lewis, G. Palmiotti, W. S. Yang

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

5 Scopus citations

Abstract

A spherical harmonics method based upon the first-order transport equation is formulated and implemented into VARIANT [1,2], a variational nodal transport code developed at Argonne National Laboratory. The spatial domain is split into hybrid finite elements, called nodes, where orthogonal polynomial spatial trial functions are used within each node and spatial Lagrange multipliers are used along the node boundaries. The internal angular approximation utilizes a complete odd-order set of spherical harmonics. Along the nodal boundaries, even and odd-order Rumyantsev interface conditions are combined with the spatial Lagrange multipliers to couple the nodes together. The new method is implemented in Cartesian x-y geometry and used to solve a fixed source benchmark problem.

Original language	English
Title of host publication	Proceedings of the PHYSOR 2004
Subtitle of host publication	The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments
Pages	1495-1503
Number of pages	9
State	Published - 2004
Externally published	Yes
Event	PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments - Chicago, IL, United States Duration: Apr 25 2004 → Apr 29 2004

Publication series

Name	Proceedings of the PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments

Conference

Conference	PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments
Country/Territory	United States
City	Chicago, IL
Period	04/25/04 → 04/29/04

Keywords

First-order form
Neutron transport
Nodal method
Spherical harmonics
VARIANT
Void node problems

Cite this

Smith, M. A., Lewis, E. E., Palmiotti, G., & Yang, W. S. (2004). A first-order spherical harmonics formulation compatible with the variational nodal method. In Proceedings of the PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments (pp. 1495-1503). (Proceedings of the PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments).

Smith, M. A. ; Lewis, E. E. ; Palmiotti, G. et al. / A first-order spherical harmonics formulation compatible with the variational nodal method. Proceedings of the PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments. 2004. pp. 1495-1503 (Proceedings of the PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments).

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title = "A first-order spherical harmonics formulation compatible with the variational nodal method",

abstract = "A spherical harmonics method based upon the first-order transport equation is formulated and implemented into VARIANT [1,2], a variational nodal transport code developed at Argonne National Laboratory. The spatial domain is split into hybrid finite elements, called nodes, where orthogonal polynomial spatial trial functions are used within each node and spatial Lagrange multipliers are used along the node boundaries. The internal angular approximation utilizes a complete odd-order set of spherical harmonics. Along the nodal boundaries, even and odd-order Rumyantsev interface conditions are combined with the spatial Lagrange multipliers to couple the nodes together. The new method is implemented in Cartesian x-y geometry and used to solve a fixed source benchmark problem.",

keywords = "First-order form, Neutron transport, Nodal method, Spherical harmonics, VARIANT, Void node problems",

author = "Smith, {M. A.} and Lewis, {E. E.} and G. Palmiotti and Yang, {W. S.}",

year = "2004",

language = "English",

isbn = "0894486837",

series = "Proceedings of the PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments",

pages = "1495--1503",

booktitle = "Proceedings of the PHYSOR 2004",

note = "PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments ; Conference date: 25-04-2004 Through 29-04-2004",

}

Smith, MA, Lewis, EE, Palmiotti, G & Yang, WS 2004, A first-order spherical harmonics formulation compatible with the variational nodal method. in Proceedings of the PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments. Proceedings of the PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments, pp. 1495-1503, PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments, Chicago, IL, United States, 04/25/04.

A first-order spherical harmonics formulation compatible with the variational nodal method. / Smith, M. A.; Lewis, E. E.; Palmiotti, G. et al.
Proceedings of the PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments. 2004. p. 1495-1503 (Proceedings of the PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments).

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

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AU - Lewis, E. E.

AU - Palmiotti, G.

AU - Yang, W. S.

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N2 - A spherical harmonics method based upon the first-order transport equation is formulated and implemented into VARIANT [1,2], a variational nodal transport code developed at Argonne National Laboratory. The spatial domain is split into hybrid finite elements, called nodes, where orthogonal polynomial spatial trial functions are used within each node and spatial Lagrange multipliers are used along the node boundaries. The internal angular approximation utilizes a complete odd-order set of spherical harmonics. Along the nodal boundaries, even and odd-order Rumyantsev interface conditions are combined with the spatial Lagrange multipliers to couple the nodes together. The new method is implemented in Cartesian x-y geometry and used to solve a fixed source benchmark problem.

AB - A spherical harmonics method based upon the first-order transport equation is formulated and implemented into VARIANT [1,2], a variational nodal transport code developed at Argonne National Laboratory. The spatial domain is split into hybrid finite elements, called nodes, where orthogonal polynomial spatial trial functions are used within each node and spatial Lagrange multipliers are used along the node boundaries. The internal angular approximation utilizes a complete odd-order set of spherical harmonics. Along the nodal boundaries, even and odd-order Rumyantsev interface conditions are combined with the spatial Lagrange multipliers to couple the nodes together. The new method is implemented in Cartesian x-y geometry and used to solve a fixed source benchmark problem.

KW - First-order form

KW - Neutron transport

KW - Nodal method

KW - Spherical harmonics

KW - VARIANT

KW - Void node problems

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T3 - Proceedings of the PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments

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BT - Proceedings of the PHYSOR 2004

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Smith MA, Lewis EE, Palmiotti G, Yang WS. A first-order spherical harmonics formulation compatible with the variational nodal method. In Proceedings of the PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments. 2004. p. 1495-1503. (Proceedings of the PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments).

A first-order spherical harmonics formulation compatible with the variational nodal method

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