Time–eigenvalue calculations in multi-region Cartesian geometry using Green’s functions

Kornreich, Drew E.; Parsons, Donald Kent

doi:10.1016/j.anucene.2005.02.004

Cited by 17 publications

(17 citation statements)

References 14 publications

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“…The first heterogeneous problem we solve are based on benchmark problems published by Kornreich and Parsons [21] as solved by the Green's function method (GFM). Their work defines a slab problem for single-speed neutrons (i.e., one group)…”

Section: Va Heterogeneous One-speed Slab Problemmentioning

confidence: 99%

Calculating Time Eigenvalues of the Neutron Transport Equation with Dynamic Mode Decomposition

McClarren

2019

Nuclear Science and Engineering

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A novel method to compute time eigenvalues of neutron transport problems is presented based on solutions to the time dependent transport equation. Using these solutions we use the dynamic mode decomposition to form an approximate transport operator. This approximate operator has eigenvalues that are mathematically related to the time eigenvalues of the neutron transport equation. This approach works for systems of any level of criticality and does not require the user to have estimates for the eigenvalues. Numerical results are presented for homogeneous and heterogeneous media. The numerical results indicate that the method finds the eigenvalues that are that contribute the most to the change in the solution over a given time range, and the eigenvalue with the largest real part is not necessarily important to the system evolution at short and intermediate times.

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Section: Va Heterogeneous One-speed Slab Problemmentioning

confidence: 99%

Calculating Time Eigenvalues of the Neutron Transport Equation with Dynamic Mode Decomposition

McClarren

2019

Nuclear Science and Engineering

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“…The difference is that the overall spatial flux response in an ADS is of interest. Still, detector responses from a pulse on an ADS reveals spatial dependences and are important for monitoring the reactivity of the configuration [33]. The TRMM obtains these spatial dependences and calculates the overall space-time response of the neutron flux for an ADS with the appropriate source.…”

Section: Accelerator-driven Subcritical Systemsmentioning

confidence: 99%

Calculating Alpha Eigenvalues and Eigenfunctions with a Markov Transition Rate Matrix Monte Carlo Method

Betzler

Kiedrowski

Martin

et al. 2018

Nuclear Science and Engineering

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“…Fission matrices are a tool usually used in Monte Carlo calculation codes to accelerate the source convergence [10][11][12][13]. This tool is designed to characterize the neutron propagation in a reactor during one generation: the Green function is the system response to a neutron pulse.…”

Section: Tfm Approach 21 Introduction Of the Usual Fission Matrixmentioning

confidence: 99%

Local correlated sampling Monte Carlo calculations in the TFM neutronics approach for spatial and point kinetics applications

Laureau

Buiron

Fontaine

2017

EPJ Nuclear Sci. Technol.

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Abstract. These studies are performed in the general framework of transient coupled calculations with accurate neutron kinetics models. This kind of application requires a modeling of the influence on the neutronics of the macroscopic cross-section evolution. Depending on the targeted accuracy, this feedback can be limited to the reactivity for point kinetics, or can take into account the redistribution of the power in the core for spatial kinetics. The local correlated sampling technique for Monte Carlo calculation presented in this paper has been developed for this purpose, i.e. estimating the influence on the neutron transport of a local variation of different parameters such as sodium density or fuel Doppler effect. This method is associated to an innovative spatial kinetics model named Transient Fission Matrix, which condenses the time-dependent Monte Carlo neutronic response in Green functions. Finally, an accurate estimation of the feedback effects on these Green functions provides an on-the-fly prediction of the flux redistribution in the core, whatever the actual perturbation shape is during the transient. This approach is also used to estimate local feedback effects for point kinetics resolution.

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Time–eigenvalue calculations in multi-region Cartesian geometry using Green’s functions

Cited by 17 publications

References 14 publications

Calculating Time Eigenvalues of the Neutron Transport Equation with Dynamic Mode Decomposition

Calculating Time Eigenvalues of the Neutron Transport Equation with Dynamic Mode Decomposition

Calculating Alpha Eigenvalues and Eigenfunctions with a Markov Transition Rate Matrix Monte Carlo Method

Local correlated sampling Monte Carlo calculations in the TFM neutronics approach for spatial and point kinetics applications

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