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Errors due to spatial differencing methods and mesh size in two-dimensional and three-dimensional discrete ordinate solutions of a typical gamma ray shielding problem are illustrated by comparing results from the DORT, TORT, and PARTISN codes. using a model geometry that is typical of spent fuel transfer and storage casks these errors were systematically investigated by varying the mesh size and differencing method. The results of this study show that the fixed-weighted and adaptive weighted diamond differencing methods in 2D problems require mesh intervals of about 0.25 mfp's for reasonable accuracy in deep penetration. The number of mesh cells required for weighted diamond difference methods severely limit the size of 3D problems that can be solved. The linear discontinuous method in PARTISN is shown to maintain numerical accuracy in 3D problems while reducing the overall computational effort by allowing larger mesh intervals. it is also shown that 3D problems exhibit differencing errors that may not readily be inferred from 2D results. Comprehensive displays of the magnitudes of spatial differencing errors in a practical shielding problem provide valuable guidance for the shielding practitioner using today's computational tools

Spatial Differencing and Mesh Sensitivity in Two- and Three-Dimensional Discrete Ordinates Codes