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.
Division Spotlight
Radiation Protection & Shielding
The Radiation Protection and Shielding Division is developing and promoting radiation protection and shielding aspects of nuclear science and technology — including interaction of nuclear radiation with materials and biological systems, instruments and techniques for the measurement of nuclear radiation fields, and radiation shield design and evaluation.
Meeting Spotlight
ANS Student Conference 2025
April 3–5, 2025
Albuquerque, NM|The University of New Mexico
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
Mar 2025
Jul 2024
Latest Journal Issues
Nuclear Science and Engineering
March 2025
Nuclear Technology
Fusion Science and Technology
April 2025
Latest News
Nuclear News 40 Under 40 discuss the future of nuclear
Seven members of the inaugural Nuclear News 40 Under 40 came together on March 4 to discuss the current state of nuclear energy and what the future might hold for science, industry, and the public in terms of nuclear development.
To hear more insights from this talented group of young professionals, watch the “40 Under 40 Roundtable: Perspectives from Nuclear’s Rising Stars” on the ANS website.
Jim E. Morel, James S. Warsa
Nuclear Science and Engineering | Volume 156 | Number 3 | July 2007 | Pages 325-342
Technical Paper | doi.org/10.13182/NSE06-13
Articles are hosted by Taylor and Francis Online.
We consider two general finite-element lumping techniques for the Sn equations with discontinuous finite-element spatial discretization and apply them to quadrilateral meshes in x-y geometry. One technique is designed to ensure a conservative approximation and is referred to as conservation preserving (CP). The other technique is designed to preserve the exact solution whenever it is contained within the trial space and is referred to as solution preserving (SP). These techniques are applied in x-y geometry on structured nonorthogonal grids using the bilinear-discontinuous finite-element approximation. The schemes are both theoretically analyzed and computationally tested. Analysis shows that the two lumping schemes are equivalent on parallelogram meshes. Computational results indicate that both techniques perform extremely well on smooth quadrilateral meshes. On nonsmooth meshes, the preserving technique retains its excellent performance while the CP technique degrades. The reasons for this degradation are discussed. Although the SP scheme has proven to be generally effective on quadrilateral meshes in x-y geometry, it is not expected to be effective for quadrilaterals in r-z geometry or for hexahedra in three-dimensional Cartesian geometry. Thus, a full lumping procedure for general nonorthogonal meshes that possesses all of the desired properties has yet to be found. For reasons that are discussed, it appears unlikely that such a procedure exists.