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Remembering ANS member Gil Brown
Brown
The nuclear community is mourning the loss of Gilbert Brown, who passed away on July 11 at the age of 77 following a battle with cancer.
Brown, an American Nuclear Society Fellow and an ANS member for nearly 50 years, joined the faculty at Lowell Technological Institute—now the University of Massachusetts–Lowell—in 1973 and remained there for the rest of his career. He eventually became director of the UMass Lowell nuclear engineering program. After his retirement, he remained an emeritus professor at the university.
Sukesh Aghara, chair of the Nuclear Engineering Department Heads Organization, noted in an email to NEDHO members and others that “Gil was a relentless advocate for nuclear energy and a deeply respected member of our professional community. He was also a kind and generous friend—and one of the reasons I ended up at UMass Lowell. He served the university with great dedication. . . . Within NEDHO, Gil was a steady presence and served for many years as our treasurer. His contributions to nuclear engineering education and to this community will be dearly missed.”
J. I. Duo, Y. Y. Azmy
Nuclear Science and Engineering | Volume 156 | Number 2 | June 2007 | Pages 139-153
Technical Paper | doi.org/10.13182/NSE05-91
Articles are hosted by Taylor and Francis Online.
Error norms for three variants of Larsen's benchmark problem are evaluated using three numerical methods for solving the discrete ordinates approximation of the neutron transport equation in multidimensional Cartesian geometry. The three variants of Larsen's test problem are concerned with the incoming flux boundary conditions: unit incoming flux on the left and bottom edges (Larsen's configuration); unit incoming flux only on the left edge; unit incoming flux only on the bottom edge. The three methods considered are the diamond-difference (DD) method, the arbitrarily high order transport (AHOT) method of the nodal type (AHOT-N), and of the characteristic type (AHOT-C). The last two methods are employed in constant, linear, and quadratic orders of spatial approximation. The cell-wise error is computed as the difference between the cell-averaged flux computed by each method and the exact value, then the L1, L2, and L error norms are calculated. The new result of this study is that while integral error norms, i.e., L1 and L2, converge to zero with mesh refinement, the cellwise L norm does not. Via numerical experiments we relate this behavior to solution discontinuity across the singular characteristic. Little difference is observed between the error norm behavior of the methods in spite of the fact that AHOT-C is locally exact, suggesting that numerical diffusion across the singular characteristic is the major source of error on the global scale. Nevertheless, increasing the order of spatial approximation in AHOT methods yields higher accuracy in the integral error norms sense. In general, the characteristic methods possess a given accuracy in a larger fraction of the number of computational cells compared to nodal methods or DD.
