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2024 ANS Annual Conference
June 16–19, 2024
Las Vegas, NV|Mandalay Bay Resort and Casino
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Latest News
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.
Michael R. Zika, Marvin L. Adams
Nuclear Science and Engineering | Volume 134 | Number 2 | February 2000 | Pages 159-170
Technical Paper | doi.org/10.13182/NSE00-A2108
Articles are hosted by Taylor and Francis Online.
The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations.Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iterating on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration.The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented.