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
September 2025
Nuclear Technology
August 2025
Fusion Science and Technology
Latest News
Deep Space: The new frontier of radiation controls
In commercial nuclear power, there has always been a deliberate tension between the regulator and the utility owner. The regulator fundamentally exists to protect the worker, and the utility, to make a profit. It is a win-win balance.
From the U.S. nuclear industry has emerged a brilliantly successful occupational nuclear safety record—largely the result of an ALARA (as low as reasonably achievable) process that has driven exposure rates down to what only a decade ago would have been considered unthinkable. In the U.S. nuclear industry, the system has accomplished an excellent, nearly seamless process that succeeds to the benefit of both employee and utility owner.
Peter G. Maginot, Jean C. Ragusa, Jim E. Morel
Nuclear Science and Engineering | Volume 179 | Number 2 | February 2015 | Pages 148-163
Technical Paper | doi.org/10.13182/NSE13-65
Articles are hosted by Taylor and Francis Online.
We examine several mass matrix lumping techniques for the discrete ordinates (SN) particle transport equations spatially discretized with arbitrary order discontinuous finite elements in one-dimensional (1-D) slab geometry. Though positive outflow angular flux is guaranteed with traditional mass matrix lumping for linear solution representations in source-free, purely absorbing 1-D slab geometry, we show that when used with higher-degree polynomial trial spaces, traditional lumping does not yield strictly positive outflows and does not increase the solution accuracy with increase in the polynomial degree of the trial space. As an alternative, we examine quadrature-based lumping strategies, which we term “self-lumping” (SL). Self-lumping creates diagonal mass matrices by using a numerical quadrature restricted to the Lagrange interpolatory points. When choosing equally spaced interpolatory points, SL is achieved through the use of closed Newton-Cotes formulas, resulting in strictly positive outflows for odd degree polynomial trial spaces in 1-D slab geometry. When selecting the interpolatory points to be the abscissas of a Gauss-Legendre or a Lobatto-Gauss-Legendre quadrature, it is possible to obtain solution representations with a strictly positive outflow in source-free pure absorber problems for any degree polynomial trial space in 1-D slab geometry. Furthermore, there is no inherent limit to local truncation error order of accuracy when using interpolatory points that correspond to Gauss-Legendre or Lobatto-Gauss-Legendre quadrature points. A single-cell analysis is performed to investigate outflow positivity and truncation error as a function of the trial space polynomial degree, the choice of interpolatory points, and the numerical integration strategy. We also verify that the single-cell local truncation error analysis translates into the expected global spatial convergence rates in multiple-cell problems.