An Efficient Exponential Directional Iterative Differencing Scheme for Three-Dimensional S_n Computations in XYZ Geometry

A new exponential spatial differencing scheme based on zeroth spatial transport moments, the exponential directional iterative (EDI) S_n scheme for three-dimensional (3-D) Cartesian geometry, is presented. The EDI scheme is a logical extension of the positive, efficient exponential directional weighted (EDW) method used in the PENTRAN parallel S_n solver in an adaptive differencing strategy. The EDI scheme uses EDW-rendered exponential coefficients as initial values to begin a fixed-point iteration to refine exponential coefficients. Iterative refinement of these coefficients typically converged in fewer than four fixed-point iterations per ordinate, and yielded more accurate angular fluxes compared to other schemes tested. Overall, the EDI scheme is an order of magnitude more accurate than EDW, and two orders of magnitude more accurate than the legacy diamond zero (DZ) scheme for a given mesh. EDI is therefore a good candidate for a fourth-level scheme in the PENTRAN adaptive sequence. The 3-D Cartesian computational cost of EDI was ~20% more than EDW, and only ~40% more than DZ. Thus, EDI renders increased accuracy using zeroth spatial transport moments in a straightforward manner for any 3-D Cartesian code. More evaluation is ongoing to determine suitability in an upgraded adaptive differencing sequence algorithm in PENTRAN.