General Expressions for Auxiliary Equations of a Nodal Formulation for Two-Dimensional Transport Calculations

摘要

A nodal approach is proposed for the solution of discrete ordinates two-dimensional fixed-source problems in Cartesian geometry. For the one-dimensional equations generated by the integration process, explicit solutions in terms of the spatial variables are derived by the analytical discrete ordinates method. The procedure does not require either iterative schemes or domain division into cells, and when associated with the level-symmetric quadrature set it leads to reduced order eigensystems. In particular, the unknown angular fluxes on the boundaries are written in terms of the elementary solutions of the one-dimensional integrated problems and a coupled system for the x and y directions is then obtained. Numerical results generated by the technique are provided and compared to those present in the literature.