### 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) |
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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 |
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Country | 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)

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## Cite this

*PHYSOR-2006 - American Nuclear Society's Topical Meeting on Reactor Physics*(Vol. 2006)