EXPONENTIAL CHARACTERISTIC SPATIAL QUADRATURE FOR DISCRETE ORDINATES RADIATION TRANSPORT WITH RECTANGULAR CELLS

The exponential characteristic (EC) spatial quadrature for discrete or dinates neutral particle transport previously introduced in slab geome try is extended here to x-y geometry with rectangular cells. The metho d is derived and compared with current methods. It is similar to the l inear characteristic (LC) quadrature (a linear-linear moments method) but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx + cy), whose parameters are r ootsolved to match the known (from the previous iteration) spatial ave rage and first moments of the source over the cell. Similarly, EC assu mes exponential distributions of flux along cell edges through which p articles enter the cell, with parameters chosen to match the average a nd first moments of flux, as passed from the adjacent, upstream cells (or as determined by boundary conditions). Like the linear adaptive (L A) method, EC is positive and nonlinear. It is more accurate than LA a nd does not require subdivision of cells. The nonlinearity has not int erfered with convergence. The exponential moment functions, which were introduced with the slab geometry method, are extended to arbitrary d imensions (numbers of arguments) and used to avoid numerical ill condi tioning. As in slab geometry, the method approaches O(Delta x(4)) glob al truncation error on fine-enough meshes, while the error is insensit ive to mesh size for coarse meshes. Performance of the method is compa red with that of the step characteristic, LC, linear nodal, step adapt ive, and LA schemes. The EC method is a strong performer with scatteri ng ratios ranging from O to 0.9 (the range tested), particularly so fo r lower scattering ratios. As in slab geometry, EC is computationally more costly per cell than current methods but can be accurate with ver y thick cells, leading to increased computational efficiency on approp riate problems.