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
Jul 2025
Jan 2025
Latest Journal Issues
Nuclear Science and Engineering
August 2025
Nuclear Technology
Fusion Science and Technology
July 2025
Latest News
DOE issues new NEPA rule and procedures—and accelerates DOME reactor testing
Meeting a deadline set in President Trump’s May 23 executive order “Reforming Nuclear Reactor Testing at the Department of Energy,” the DOE on June 30 updated information on its National Environmental Policy Act (NEPA) rulemaking and implementation procedures and published on its website an interim final rule that rescinds existing regulations alongside new implementing procedures.
James S. Warsa, Todd A. Wareing, Jim E. Morel
Nuclear Science and Engineering | Volume 147 | Number 3 | July 2004 | Pages 218-248
Technical Paper | doi.org/10.13182/NSE02-14
Articles are hosted by Taylor and Francis Online.
A loss in the effectiveness of diffusion synthetic acceleration (DSA) schemes has been observed with certain SN discretizations on two-dimensional Cartesian grids in the presence of material discontinuities. We will present more evidence supporting the conjecture that DSA effectiveness will degrade for multidimensional problems with discontinuous total cross sections, regardless of the particular physical configuration or spatial discretization. Fourier analysis and numerical experiments help us identify a set of representative problems for which established DSA schemes are ineffective, focusing on diffusive problems for which DSA is most needed. We consider a lumped, linear discontinuous spatial discretization of the SN transport equation on three-dimensional, unstructured tetrahedral meshes and look at a fully consistent and a "partially consistent" DSA method for this discretization. The effectiveness of both methods is shown to degrade significantly. A Fourier analysis of the fully consistent DSA scheme in the limit of decreasing cell optical thickness supports the view that the DSA itself is failing when material discontinuities are present in a problem. We show that a Krylov iterative method, preconditioned with DSA, is an effective remedy that can be used to efficiently compute solutions for this class of problems. We show that as a preconditioner to the Krylov method, a partially consistent DSA method is more than adequate. In fact, it is preferable to a fully consistent method because the partially consistent method is based on a continuous finite element discretization of the diffusion equation that can be solved relatively easily. The Krylov method can be implemented in terms of the original SN source iteration coding with only slight modification. Results from numerical experiments show that replacing source iteration with a preconditioned Krylov method can efficiently solve problems that are virtually intractable with accelerated source iteration.