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
Latest News
ANS joins others in seeking to discuss SNF/HLW impasse
The American Nuclear Society joined seven other organizations to send a letter to Energy Secretary Christopher Wright on July 8, asking to meet with him to discuss “the restoration of a highly functioning program to meet DOE’s legal responsibility to manage and dispose of the nation’s commercial and legacy defense spent nuclear fuel (SNF) and high-level radioactive waste (HLW).”
Deokjung Lee, Thomas J. Downar, Yonghee Kim
Nuclear Science and Engineering | Volume 147 | Number 2 | June 2004 | Pages 127-147
Technical Paper | doi.org/10.13182/NSE03-64
Articles are hosted by Taylor and Francis Online.
The convergence rates of the nonlinear coarse-mesh finite difference (CMFD) method and the coarse-mesh rebalance (CMR) method are derived analytically for one-dimensional, one-group solutions of the fixed-source diffusion problem in a nonmultiplying infinite homogeneous medium. The derivation was performed by linearizing the nonlinear algorithm and by applying Fourier error analysis to the linearized algorithm. The mesh size measured in units of the diffusion length is shown to be a dominant parameter for the convergence rate and for the stability of the iterative algorithms. For a small mesh size problem, the nonlinear CMFD is shown to be a more effective acceleration method than CMR. Both CMR and two-node CMFD algorithms are shown to be unconditionally stable. However, the one-node CMFD becomes unstable for large mesh sizes. To remedy this instability, an underrelaxation of the current correction factor for the one-node CMFD method is successfully introduced, and the domain of stability is significantly expanded. Furthermore, the optimum underrelaxation parameter is analytically derived, and the one-node CMFD with the optimum relaxation is shown to be unconditionally stable.