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
2026 Annual Conference
May 31–June 3, 2026
Denver, CO|Sheraton Denver
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
Dec 2025
Jul 2025
Latest Journal Issues
Nuclear Science and Engineering
January 2026
Nuclear Technology
December 2025
Fusion Science and Technology
November 2025
Latest News
What’s the most difficult question you’ve been asked as a maintenance instructor?
Blye Widmar
"Where are the prints?!"
This was the final question in an onslaught of verbal feedback, comments, and critiques I received from my students back in 2019. I had two years of instructor experience and was teaching a class that had been meticulously rehearsed in preparation for an accreditation visit. I knew the training material well and transferred that knowledge effectively enough for all the students to pass the class. As we wrapped up, I asked the students how they felt about my first big system-level class, and they did not hold back.
“Why was the exam from memory when we don’t work from memory in the plant?” “Why didn’t we refer to the vendor documents?” “Why didn’t we practice more on the mock-up?” And so on.
Uncheol Shin, Warren F. Miller, Jr.
Nuclear Science and Engineering | Volume 128 | Number 1 | January 1998 | Pages 27-46
Technical Paper | doi.org/10.13182/NSE98-A1943
Articles are hosted by Taylor and Francis Online.
Using an asymptotic expansion, we found that the modified time-dependent simplified P2 (SP2) equations are robust, high-order, asymptotic approximations to the time-dependent transport equation in a physical regime in which the conventional time-dependent diffusion equation is the leading-order approximation. Using diffusion limit analysis, we also asymptotically compared three competitive time-dependent equations (the telegrapher's equation, the time-dependent SP2 equations, and the time-dependent simplified even-parity equation). As a result, we found that the time-dependent SP2 equations contain higher-order asymptotic approximations to the time-dependent transport equation than the other competitive equations. The numerical results confirm that, in the vast majority of cases, the time-dependent SP2 solutions are significantly more accurate than the time-dependent diffusion and the telegrapher's solutions. We have also shown that the time-dependent SP2 equations have excellent characteristics such as rotational invariance (which means no ray effect), good diffusion limit behavior, guaranteed positivity in diffusive regimes, and significant accuracy, even in deep-penetration problems. Through computer-running-time tests, we have shown that the time-dependent SP2 equations can be solved with significantly less computational effort than the conventionally used, time-dependent SN equations (for N > 2) and almost as fast as the time-dependent diffusion equation. From all these results, we conclude that the time-dependent SP2 equations should be considered as an important competitor for an improved approximate transport equation solver. Such computationally efficient time-dependent transport models are especially important for problems requiring enhanced computational efficiency, such as neutronics/fluid-dynamics coupled problems that arise in the analyses of hypothetical nuclear reactor accidents.
