A first-order integral method developed for the VARIANT code

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

A first-order integral method developed for the VARIANT code

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

^*Corresponding author for this work

Mechanical Engineering

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

Abstract

A first order nodal integral method using spherical harmonic interface conditions is formulated and implemented into VARIANT [1-3], 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 is weighted with a complete odd-order spherical harmonics set and numerically integrated using a standard angular quadrature. Along the nodal boundaries, even-order Rumyantsev interface conditions are combined with the spatial Lagrange multipliers to couple the nodes together. The new method is implemented in Cartesian geometry and used to solve a fixed source two-dimensional benchmark problem.

Original language	English (US)
Title of host publication	PHYSOR-2006 - American Nuclear Society's Topical Meeting on Reactor Physics
Volume	2006
State	Published - Dec 1 2006
Event	PHYSOR-2006 - American Nuclear Society's Topical Meeting on Reactor Physics - Vancouver, BC, Canada Duration: Sep 10 2006 → Sep 14 2006

Other

Other	PHYSOR-2006 - American Nuclear Society's Topical Meeting on Reactor Physics
Country/Territory	Canada
City	Vancouver, BC
Period	9/10/06 → 9/14/06

Keywords

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

ASJC Scopus subject areas

Engineering(all)

Cite this

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title = "A first-order integral method developed for the VARIANT code",

abstract = "A first order nodal integral method using spherical harmonic interface conditions is formulated and implemented into VARIANT [1-3], 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 is weighted with a complete odd-order spherical harmonics set and numerically integrated using a standard angular quadrature. Along the nodal boundaries, even-order Rumyantsev interface conditions are combined with the spatial Lagrange multipliers to couple the nodes together. The new method is implemented in Cartesian geometry and used to solve a fixed source two-dimensional benchmark problem.",

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

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

year = "2006",

month = dec,

day = "1",

language = "English (US)",

isbn = "0894486977",

volume = "2006",

booktitle = "PHYSOR-2006 - American Nuclear Society's Topical Meeting on Reactor Physics",

note = "PHYSOR-2006 - American Nuclear Society's Topical Meeting on Reactor Physics ; Conference date: 10-09-2006 Through 14-09-2006",

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TY - GEN

T1 - A first-order integral method developed for the VARIANT code

AU - Smith, M. A.

AU - Lewis, Elmer E

AU - Palmiotti, G.

AU - Yang, W. S.

PY - 2006/12/1

Y1 - 2006/12/1

N2 - A first order nodal integral method using spherical harmonic interface conditions is formulated and implemented into VARIANT [1-3], 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 is weighted with a complete odd-order spherical harmonics set and numerically integrated using a standard angular quadrature. Along the nodal boundaries, even-order Rumyantsev interface conditions are combined with the spatial Lagrange multipliers to couple the nodes together. The new method is implemented in Cartesian geometry and used to solve a fixed source two-dimensional benchmark problem.

AB - A first order nodal integral method using spherical harmonic interface conditions is formulated and implemented into VARIANT [1-3], 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 is weighted with a complete odd-order spherical harmonics set and numerically integrated using a standard angular quadrature. Along the nodal boundaries, even-order Rumyantsev interface conditions are combined with the spatial Lagrange multipliers to couple the nodes together. The new method is implemented in Cartesian geometry and used to solve a fixed source two-dimensional benchmark problem.

KW - First-order form

KW - Neutron transport

KW - Nodal method

KW - Spherical harmonics

KW - VARIANT

KW - Void region problems

UR - http://www.scopus.com/inward/record.url?scp=33847187390&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33847187390&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33847187390

SN - 0894486977

SN - 9780894486975

VL - 2006

BT - PHYSOR-2006 - American Nuclear Society's Topical Meeting on Reactor Physics

T2 - PHYSOR-2006 - American Nuclear Society's Topical Meeting on Reactor Physics

Y2 - 10 September 2006 through 14 September 2006

ER -

A first-order integral method developed for the VARIANT code

Abstract

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Keywords

ASJC Scopus subject areas

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