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Division Spotlight
Reactor Physics
The division's objectives are to promote the advancement of knowledge and understanding of the fundamental physical phenomena characterizing nuclear reactors and other nuclear systems. The division encourages research and disseminates information through meetings and publications. Areas of technical interest include nuclear data, particle interactions and transport, reactor and nuclear systems analysis, methods, design, validation and operating experience and standards. The Wigner Award heads the awards program.
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Utility Working Conference and Vendor Technology Expo (UWC 2024)
August 4–7, 2024
Marco Island, FL|JW Marriott Marco Island
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!
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Fusion Science and Technology
Latest News
Taking shape: Fusion energy ecosystems built with public-private partnerships
It’s possible to describe fusion in simple terms: heat and squeeze small atoms to get abundant clean energy. But there’s nothing simple about getting fusion ready for the grid.
Private developers, national lab and university researchers, suppliers, and end users working toward that goal are developing a range of complex technologies to reach fusion temperatures and pressures, confounded by science and technology gaps linked to plasma behavior; materials, diagnostics, and electronics for extreme environments; fuel cycle sustainability; and economics.
Erin D. Fichtl, James S. Warsa, Jeffery D. Densmore
Nuclear Science and Engineering | Volume 165 | Number 3 | July 2010 | Pages 331-341
Technical Paper | doi.org/10.13182/NSE09-51
Articles are hosted by Taylor and Francis Online.
Under some circumstances, spatial discretizations of the SN transport equation will lead to negativity in the scalar flux; therefore, negative-flux fixup schemes are often employed to ensure that the flux is positive. The nonlinear nature of these schemes precludes the use of powerful linear iterative solvers such as Krylov methods; thus, solutions are generally computed using so-called source iteration (SI), which is a simple fixed-point iteration. In this paper, we use Newton's method to solve fixed-source SN transport problems with negative-flux fixup, for which the analytic form of the Jacobian is shown to be nonsingular. It is necessary to invert the Jacobian at each Newton iteration. Generally, an exact inversion is prohibitively expensive and furthermore is not necessary for convergence of Newton's method. In the inexact Newton-Krylov method, the Jacobian is inverted using a Krylov method, which completes at some prescribed tolerance. This tolerance may be quite large in the initial stages of the Newton iteration. In this paper, we compare the use of the exact Jacobian with two approximations of the Jacobian in the inexact Newton-Krylov method. The first approximation is a finite difference approximation. The second is that used in the Jacobian-free Newton-Krylov (JFNK) method, which performs a finite difference approximation without actually generating the Jacobian itself. Numerical results comparing standard SI with the three methods demonstrate that Newton-Krylov can outperform SI, particularly for diffusive materials. The results also show that the additional level of approximation introduced by the JFNK approach does not adversely affect convergence, indicating that JFNK will be robust and efficient in large-scale applications.