The linear characteristic (LC) method is extended to unstructured meshes of
tetrahedral cells in three-dimensional Cartesian coordinates. For each ord
inate in a discrete ordinates sweep, Each cell is split into subcells along
a line parallel to the ordinate. Direct affine transformations among appro
priate oblique Cartesian coordinate systems for the faces and interior of e
ach cell and subcell are used to simplify the characteristic transport thro
ugh each subcell. This approach is straightforward and eliminates computati
onally expensive trigonometric functions. An efficient and well-conditioned
technique for evaluating the required integral moments of exponential func
tions is presented Various test problems are used to demonstrate (a) the ap
proach to cubic convergence as the mesh is refined (b) insensitivity to the
details of irregular meshes, and (c) numerical robustness. These tests als
o 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/disc
rete ordinates method together with MCNP, is used to distinguish between er
ror 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.