The Verification of 3 Dimensional Nodal Kinetics Code ANCK Using Transient Benchmark Problems

Aoki, Shigeaki; Suemura, Takayuki; Ogawa, Junto; Takeda, Toshikazu

doi:10.1080/18811248.2007.9711323

Cited by 12 publications

(1 citation statement)

References 3 publications

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“…2,[9][10][11] The conventional methods except for SCM apply the time difference approximation to the space-dependent kinetics equation, which is already discretized in space. Since most of the above methods are based on the (partly) implicit scheme, inhomogeneous linear equations in space (and energy) should be solved with an iteration method.…”

Section: Introductionmentioning

confidence: 99%

Explicit Time Integration Scheme Using Krylov Subspace Method for Reactor Kinetics Equation

Ban

Endo

Yamamoto

et al. 2011

Journal of Nuclear Science and Technology

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The spatial discretization form of the space-dependent reactor kinetics equation is a first-order simultaneous ordinary differential equation in time. Conventional numerical methods of the space-dependent kinetics equation, i.e., the generalized Runge-Kutta method, the implicit method (backward Euler method), and the Theta method, are based on the time difference approximation. However, the present study adopts the analytical solution of the space-dependent kinetics equation expressed by the matrix exponential and no time difference approximation is used. In this context, our present approach is classified as an explicit method in which no iteration calculation on space and energy is necessary. The Krylov subspace method is used to evaluate the matrix exponential observed in the solution of the spatially discretized space-dependent kinetics equation. The Krylov subspace method is implemented into a space-dependent kinetics solver. In order to examine the effectiveness of the Krylov subspace method, the TWIGL benchmark problem is analyzed as a verification calculation. The calculation results show the effectiveness of the present method especially in the step reactivity perturbation.

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Section: Introductionmentioning

confidence: 99%