Split-cell exponential characteristic transport method for unstructured tetrahedral meshes

The nonlinear, exponential characteristic (EC) method is extended to unstru ctured meshes of tetrahedral cells in three-dimensional Cartesian coordinat es. The split-cell approach developed for the linear characteristic (LC) me thod on such meshes is used. Exponential distributions of the source within a cell and of the inflow flux on upstream faces of the cell are assumed. T he coefficients of these distributions are determined by nonlinear root sol ving so as to match the zeroth and first moments of the source or entering flux Good conditioning is achieved by casting the formulas for the moments of the source, inflow flux, and solution flux as stems of positive function s and by using accurate and robust algorithms for evaluation of those funct ions. Various test problems are used to compare the performance of the EC a nd LC methods. The EC method is somewhat less accurate than the LC method i n regions of net out leakage brit is strictly positive and retains good acc uracy with optically thick cells, as in shielding problems, unlike the LC m ethod. The computational cost per cell is greater for the EC method bur the use of substantially coarser meshes can make the EC method less expensive in total cost. The EC method, unlike the LC method, may fail if negative cr oss sections or angular quadrature weights are used. It is concluded that t he EC and LC methods should be practical, reliable, and complimentary schem es for these meshes.