Angular eigenfunctions for elliptical problems in three- and four-region domains with interior corners
Dan Gabriel Cacuci, Mihaela Ionescu‐Bujor · Transactions of the American Nuclear Society · 1996
Multiregion two-dimensional domains occur in many problems, including reactor core models for neutronics calculations. The geometries typically encountered in such problems are rectangular or hexagonal and typically involve interior corners at the intersections between domains (e.g., homogenized subassemblies) with distinct material properties. The analytical solution of the multigroup neutron diffusion equation (MGDE) at and around such corners has been presented in Ref. 1, where it was shown that the neutron flux for the g`th energy group has the form {Phi}{sup g}r,{theta} = {Sigma}{sub j} f{sub jg} (G;r)T{sub j}(g;{theta}), where G denotes the fact that the functions f{sub jg} depend on the material properties (i.e., diffusion coefficients and cross sections) pertaining to all of the energy groups. Although the expressions for the radial functions f{sub jg} (G; r) were presented, the specific expressions for the angular eigenfunctions T{sub j} (g; {theta}) were not presented there. This was because these angular eigenfunctions are generally applicable to all elliptical problems (i.e., problems that involve a Laplace-type operator) and not only to the MGDE. It is the purpose of this paper to present the exact expressions of these angular eigenfunctions for two of the most commonly encountered geometries in engineering (including reactor neutronics) problems,more » namely, three-region hexagonal and four-region rectangular geometry, respectively.« less