Split-Cell, Linear Characteristic Transport Method for Unstructured Tetrahedral Meshes

Abstract

The linear characteristic (LC) method is extended to unstructured meshes of tetrahedral cells in three-dimensional Cartesian coordinates. For each ordinate in a discrete ordinates sweep, each cell is split into subcells along a line parallel to the ordinate. Direct affine transformations among appropriate oblique Cartesian coordinate systems for the faces and interior of each cell and subcell are used to simplify the characteristic transport through each subcell. This approach is straightforward and eliminates computationally expensive trigonometric functions. An efficient and well-conditioned technique for evaluating the required integral moments of exponential functions is presented. Various test problems are used to demonstrate (a) the approach to cubic convergence as the mesh is refined, (b) insensitivity to the details of irregular meshes, and (c) numerical robustness. These tests also show that meshes should represent volumes of regions with curved as well as planar boundaries exactly and that cells should have optical thicknesses throughout the mesh that are more or less equal. A hybrid Monte Carlo/discrete ordinates method, together with MCNP, is used to distinguish between error introduced by the angular and the spatial quadratures. We conclude that the LC method should be a practical and reliable scheme for these meshes, presuming that the cells are not optically too thick.