Variational nodal formulation for the spherical harmonics equations

Journal Article · Thu Feb 01 04:00:00 EST 1996 · Nuclear Science and Engineering

DOI:https://doi.org/10.13182/NSE96-1· OSTI ID:218502

Lewis, E E ^[1]; Carrico, C B ^[2]; Palmiotti, G ^[3]

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1. Northwestern Univ., Evanston, IL (United States). Dept. of Mechanical Engineering
2. Argonne National Lab., IL (United States). Reactor Analysis Div.
3. Commissariat a l`Energie Atomique, Saint-Paul-lez-Durance (France). Centre d`Etudes Nucleaires de Cadarache

The variational nodal formulation of the neutron transport equation is generalized to provide spherical harmonics approximations of arbitrary odd order. The even angular parity trial functions within the nodes are complemented by new odd angular parity trial functions at the node interfaces. These are derived from the spherical harmonic continuity conditions presented in the classical work of Rumyantsev. The Y{sub n{+-}n} terms are absent for all odd n in the resulting odd-parity trial function sets. This result is shown to be equivalent to requiring the variational nodal matrix that couples even- and odd-parity angular trial functions to be of full rank and yields vacuum and reflected boundary conditions as well as nodal interface conditions within the framework of the variational formulation. Nodal P{sub 1}, P{sub 3}, and P{sub 5} approximations are implemented in the Argonne National Laboratory code VARIANT, utilizing the existing spatial trial functions in x-y geometry. The accuracy of the approximations is demonstrated on model fixed source and few-group eigenvalue problems. The new interface trial functions have no effect on P{sub 1} approximations and yield P{sub 3} results that differ very little from those obtained with existing trial functions, even where the P{sub 5} approximation leads to further improvement. More significantly, the new trial functions allow P{sub 5} or higher order algorithms to be implemented in a consistent straightforward manner.

• Sponsoring Organization: USDOE
• OSTI ID: 218502
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 2 Vol. 122; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ACCURACY
COMPARATIVE EVALUATIONS
NEUTRON TRANSPORT THEORY
NODAL EXPANSION METHOD
SPHERICAL HARMONICS METHOD
THEORETICAL DATA
V CODES
VARIATIONAL METHODS