Closed linear one-cell functional spatial approximations

Abstract

Closed linear one-cell functional (closed LOF) methods are introduced as a class of discrete spatial approximations to the discrete-ordinate equations for anisotropically scattering monoenergetic transport in slab geometry. It is shown that most spatial approximations currently used or suggested for use, for this class of problems, are specific realizations of closed LOF methods. An appropriate concept of consistency is introduced for closed LOF methods. It is shown that a consistent closed LOF method is asymptotically a finite-difference method, in the sense that the approximating equations can be expressed in terms of approximations to the cell-edge fluxes, for sufficiently fine meshes. Further questions related to closed LOF methods are suggested for future study.