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Securing the advanced reactor fleet
Physical protection accounts for a significant portion of a nuclear power plant’s operational costs. As the U.S. moves toward smaller and safer advanced reactors, similar protection strategies could prove cost prohibitive. For tomorrow’s small modular reactors and microreactors, security costs must remain appropriate to the size of the reactor for economical operation.
Marvin L. Adams
Nuclear Science and Engineering | Volume 137 | Number 3 | March 2001 | Pages 298-333
Technical Paper | doi.org/10.13182/NSE00-41
Articles are hosted by Taylor and Francis Online.
The performance of discontinuous finite element methods (DFEMs) on problems that contain optically thick diffusive regions is analyzed and tested. The asymptotic analysis is quite general; it holds for an entire family of DFEMs in slab, XY, and XYZ geometries on arbitrarily connected polygonal or polyhedral spatial grids. The main contribution of the work is a theory that predicts and explains how DFEMs behave when applied to thick diffusive regions. It is well known that in the interior of such a region, the exact transport solution satisfies (to leading order) a diffusion equation, with boundary conditions that are known. Thus, in the interiors of such regions, the ideal discretized transport solution would satisfy (to leading order) an accurate discretization of the same diffusion equation and boundary conditions. The theory predicts that one class of DFEMs, which we call "zero-resolution" methods, fails dramatically in thick diffusive regions, yielding solutions that are completely meaningless. Another class - full-resolution methods - has leading-order solutions that satisfy discretizations of the correct diffusion equation. Full-resolution DFEMs are classified according to several categories of performance: continuity, robustness, accuracy, and boundary condition. Certain kinds of lumping, some of which are believed to be new, improve DFEM behavior in the continuity, robustness, and boundary-condition categories. Theoretical results are illustrated using different variations of linear and bilinear DFEMs on several test problems in XY geometry. In every case, numerical results agree precisely with the predictions of the asymptotic theory.