Calculation of the eigenfunctions of the two-group neutron diffusion equation and application to modal decomposition of BWR instabilities

Zinzani, Filippo; Demazière, Christophe; Sunde, Carl

doi:10.1016/j.anucene.2008.05.004

Cited by 19 publications

(9 citation statements)

References 22 publications

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“…This was shown by [90]. Since it is hard to calculate this optimal subspace size a-priori and that larger memory requirements prohibit storing many vectors, the situation where limited subspace size is prescribed has been considered here.…”

Section: Chapter 6 Application Of Karma To Alternate Problems157mentioning

confidence: 99%

“…The accuracy of the subsequent modes may be affected if the computed modes have a large residual error that can propagate in the computation of subsequent higher modes and corrupts the deflated linear system (in [90], a tolerance close to machine precision was used).…”

Section: Chapter 6 Application Of Karma To Alternate Problems140mentioning

confidence: 99%

“…In the work by Demaziere [90], the traditional PI method is used to calculate several eigenmodes with Wielandt deflation but this procedure involves the CHAPTER 6. APPLICATION OF KARMA TO ALTERNATE PROBLEMS141 necessity for calculating the forward and adjoint eigenvector for each mode.…”

Section: Chapter 6 Application Of Karma To Alternate Problems140mentioning

confidence: 99%

“…Recently, Krylov-subspace iteration methods have been proposed as alternatives to the PI method to compute several dominant eigenmodes, e.g., the subspace projection method with locking of converged eigenvectors [93], the explicit Arnoldi iteration [73,90], the implicit restarted Arnoldi method (IRAM) [94,95,96,97,98], the Jacobi-Davidson method [99,88,100]. Subspace methods for eigenproblems have been described and reviewed by several authors in the mathematics and numerical analysis communities; see, for instance, [101,102].…”

Section: Chapter 6 Application Of Karma To Alternate Problems137mentioning

confidence: 99%

“…Reactor instabilities are local power variations occurring due to periodic flow oscillations and can sometimes grow undamped. In stability studies, not only the fundamental mode but also higher-order eigenmodes are needed in order to predict core behavior accurately.Fast and accurate numerical methods to obtain the fundamental mode and to perform modal analysis for reactor instabilities are an ongoing topic of research; see, e.g., [86,87,88,89,90]. In the current section, we underscore the link between all eigenproblems with constrained non-linear optimization problems and take advantage of this reformulation to use the Newton's method for solving the eigenproblems.…”

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confidence: 99%

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Neutronic/Thermalhydraulic Coupling Technigues for Sodium Cooled Fast Reactor Simulations

Ragusa¹,

Siegel²,

Ruggieri³

2010

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Executive SummaryThe objective of this project was to test new coupling algorithms and enable efficient and scalable multi-physics simulations of advanced nuclear reactors, with considerations regarding the implementation of such algorithms in massively parallel environments. Numerical tests were carried out to verify the proposed approach and the examples included some reactor transients. The project was directly related to the Sodium Fast Reactor program element of the Generation IV Nuclear Energy Systems Initiative and the Advanced Fuel cycle Initiative, and, supported the requirement of high-fidelity simulation as a mean of achieving the goals of the presidential Global Nuclear Energy Partnership (GNEP) vision.For decades, the modeling of nuclear cores has been divided into several distinct domains of physics: neutronics, hydraulics, heat transfer, … Yet, these physical models describe physical processes that are tightly intertwined and rely heavily on the solution field of one another. In the last decade or so, various existing mono-disciplinary codes have been coupled together in a naive "black-box" fashion, where the output of one code serves as the input of another code, producing nonlinearly inconsistent multiphysics solutions. Such schemes, which are still the main coupling paradigm today for solving nonlinear nuclear reactor physics equations, are based on a linearization of the coupling terms that is never resolved and that can lead to a loss of accuracy and stability in the solution procedure. In order to address the inconsistencies of traditional coupling strategies, a 3-D test-bed code based on reduced physical models has been developed. It includes several physic components, namely, multigroup neutron diffusion, monophasic fluid conservation laws (mass, momentum, energy), nonlinear heat conduction. This test-bed code was used to demonstrate the loss of accuracy order due to traditional operator-split techniques used in conventional coupling schemes; to implement Jacobian-free full resolution coupling schemes; to develop adaptive preconditioning techniques; and to investigate high-order time discretizations and adaptive time stepping strategies. The test-bed code employs state-of-the-art algorithms and libraries, namely the Jacobian0free Newton-Krylov technique to solve consistently fully implicit tightly coupled simulations and the ANL's PETSc library of linear and nonlinear solvers for scalability. We have demonstrated that the multiphysics solution procedure yields highly accurate solutions in space and time and is amenable for space/time adaptivity. This portion of the work is discussed in Part A of this report.It is widely agreed that high fidelity simulations is an utmost important tool for the conception, design and validation of complex physical systems such as nuclear reactors. Examples of such thrust can be seen in the ASCI program and the SciDAC program. GNEP strongly advocates the development of the next-generation simulation software with a far wider range of applicability than conven...

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Section: Chapter 6 Application Of Karma To Alternate Problems157mentioning

confidence: 99%

Section: Chapter 6 Application Of Karma To Alternate Problems140mentioning

confidence: 99%

Section: Chapter 6 Application Of Karma To Alternate Problems140mentioning

confidence: 99%