### 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 (US) |
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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 - Dec 1 2004 |

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 |
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### Other

Other | PHYSOR 2004: The Physics of Fuel Cycles and Advanced Nuclear Systems - Global Developments |
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Country | United States |

City | Chicago, IL |

Period | 4/25/04 → 4/29/04 |

### Keywords

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

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

*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).