ANS is committed to advancing, fostering, and promoting the development and application of nuclear sciences and technologies to benefit society.
Explore the many uses for nuclear science and its impact on energy, the environment, healthcare, food, and more.
Explore membership for yourself or for your organization.
Conference Spotlight
Nuclear Energy Conference & Expo (NECX)
September 8–11, 2025
Atlanta, GA|Atlanta Marriott Marquis
Standards Program
The Standards Committee is responsible for the development and maintenance of voluntary consensus standards that address the design, analysis, and operation of components, systems, and facilities related to the application of nuclear science and technology. Find out What’s New, check out the Standards Store, or Get Involved today!
Latest Magazine Issues
Aug 2025
Jan 2025
Latest Journal Issues
Nuclear Science and Engineering
September 2025
Nuclear Technology
Fusion Science and Technology
August 2025
Latest News
Powering the future: How the DOE is fueling nuclear fuel cycle research and development
As global interest in nuclear energy surges, the United States must remain at the forefront of research and development to ensure national energy security, advance nuclear technologies, and promote international cooperation on safety and nonproliferation. A crucial step in achieving this is analyzing how funding and resources are allocated to better understand how to direct future research and development. The Department of Energy has spearheaded this effort by funding hundreds of research projects across the country through the Nuclear Energy University Program (NEUP). This initiative has empowered dozens of universities to collaborate toward a nuclear-friendly future.
Bojan G. Petrović, Alireza Haghighat
Nuclear Science and Engineering | Volume 124 | Number 1 | September 1996 | Pages 31-62
Technical Paper | doi.org/10.13182/NSE96-A24222
Articles are hosted by Taylor and Francis Online.
Recent pressure vessel fast fluence calculations have revealed numerical difficulties (spatial oscillations) in the SN solutions, which have persisted in spite of mesh refinement. It is demonstrated that other shielding/deep-penetration applications may be affected; in fact, any SN solution in which the uncollided flux component is significant is likely to exhibit such difficulties. Test problems have been designed to characterize and understand numerical difficulties. Main analyses are performed using the diamond-difference (DD) scheme, which is linear and forms the basis for other (more complex) low-order differencing schemes. The genesis of oscillations is shown to be related to several effects specific for multidimensional geometries as follows: ambiguity in the interpretation of boundary conditions, discontinuities, and different directions of particle streaming and differencing. It has further been explained why the mesh refinement does not produce the intuitively expected results. Other low-order differencing schemes (e.g., the DD with negative flux fixup and the θ-weighted) may partly remedy the situation by reducing the oscillations or by eliminating the oscillations at a cost of “oversmoothing” the results everywhere (e.g., the zero-weighted scheme). These schemes provide more robust solutions, but the inherent difficulties (although reduced) still remain. Types of discontinuities that trigger the oscillations are also examined; it is difficult to envisage an actual practical application free of such discontinuities. The magnitude of numerical difficulties (oscillations) and their practical relevance will depend on all SN model features, the differencing scheme being used, and the application requirements, but this study has shown that they are inherent to multidimensional finite-difference SN algorithms.
