Angular eigenfunctions for elliptical problems in two-region domains with interior corners

Journal Article · Tue Dec 31 04:00:00 EST 1996 · Transactions of the American Nuclear Society

OSTI ID:436892

Cacuci, D G ^[1]

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1. Univ. of Karlsruhe (Germany)

Two-region domains are frequently encountered in neutronics calculations of nuclear reactor cores-both in hexagonal and rectangular geometries. A two-region domain that is typical of both geometries is depicted. In particular, the angle a would take on the values {alpha} = 2{pi}/3 and {alpha} = {pi}/4 in hexagonal and rectangular geometry, respectively. The analytical solution of the multigroup diffusion equation (MGDE) at interior corners in two-dimensional multiregion domains has been derived. The explicit expressions of the angular eigenfunctions for two-region domains, though, were not presented there because these eigenfunctions are generally applicable for solving not only the MGDE but also for solving any elliptical problems (i.e., problems involving Laplace-type operators) in a two-region domain. It is the aim of this paper to present the complete expressions of these angular eigenfunctions - first for an arbitrary angle a and then for the two most often encountered geometries in nuclear reactor design, namely, hexagonal ({alpha} = 2{pi}/3) and rectangular ({alpha} = {pi}/4) geometries. These results are new and as already mentioned-significant for all elliptical problems in two-dimensional two-region domains.

• OSTI ID: 436892
• Report Number(s): CONF-9606116--
• Journal Information: Transactions of the American Nuclear Society, Journal Name: Transactions of the American Nuclear Society Vol. 74; ISSN TANSAO; ISSN 0003-018X
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
99 GENERAL AND MISCELLANEOUS
ANALYTICAL SOLUTION
EIGENFUNCTIONS
EIGENVALUES
HEXAGONAL CONFIGURATION
MATHEMATICAL MODELS
MULTIGROUP THEORY
NEUTRON DIFFUSION EQUATION
REACTOR CORES
RECTANGULAR CONFIGURATION