Asymptotic Diffusion Limits of the Multigroup Neutron Transport Equations

Abstract

In this paper, the standard multigroup neutron diffusion equations are derived as an asymptotic approximation to the multigroup neutron transport equations. The asymptotic analysis employs a scaling that (1) is suggested by the multigroup neutron diffusion equations themselves and (2) generalizes the long-known asymptotic scaling for monoenergetic transport problems. Two other asymptotic scalings of the multigroup transport equations are also considered, both of which lead to a new “group-collapsed” (monoenergetic) “equilibrium” diffusion approximation. The standard multigroup and equilibrium diffusion approximations are shown to preserve certain nonasymptotic properties of the multigroup transport equations. Generalizations of the analyses in this paper, and possible practical applications, are discussed.

Keywords:

• Multigroup transport
• multigroup diffusion
• asymptotic approximation
• asymptotic analysis

Acknowledgments

I would like to thank Todd Urbatch, who asked me to give a plenary talk (on this work) at the M&C 2021 conference, and to Dmitriy Anistratov and the other members of the M&C 2021 Organizing Committee who helped make the conference a reality.

I would also like to thank Jeff Densmore, who read an earlier version of this paper and suggested substantive improvements. Finally, I wish to express my gratitude to Nick Adamowicz, who in a discussion last summer asked some exceptionally stimulating questions that led to the work presented in this paper.

Disclosure Statement

No potential conflict of interest was reported by the author(s).