Numerical solution of matrix exponential in burn-up equation using mini-max polynomial approximation

Kawamoto, Yosuke; Chiba, Go; Tsuji, Masashi; Narabayashi, Tadashi

doi:10.1016/j.anucene.2015.02.015

Cited by 30 publications

(9 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nuclides transmutation calculations are carried out with the reference detail chain model or the simplified chain model as mentioned above. Nuclides transmutation equations including adjoint problems in DPT are solved by the matrix exponential method with the mini-max polynomial approximation method [18,19]. For LWR assembly calculations, the predictor-corrector method is employed.…”

Section: Sensitivity Calculations With the Depletion Perturbation Theorymentioning

confidence: 99%

Sensitivity and uncertainty analyses of fission product nuclide inventories for passive gamma spectroscopy

Chiba

Honta

2020

Journal of Nuclear Science and Technology

Self Cite

View full text Add to dashboard Cite

The passive gamma spectroscopy (PGS) is a useful technique to extract information on spent nuclear fuels without any destructive actions. This method requires a correlation between number densities (NDs) of target nuclides, and it is generally estimated by numerical simulation. Therefore, prediction accuracy of these nuclides generations is one of key issues in PGS. Nuclear data used in nuclear fuel depletion calculations is one of dominant uncertainty sources, so we quantify nuclear data-induced uncertainties of NDs of six fission product nuclides, which are important in PGS: Ce-144, Cs-134, -137, Ru-106, Sb-125 and Eu-154. Generation mechanisms of these nuclides are quantitatively investigated through sensitivities of these NDs to nuclear data, which can be calculated by the depletion perturbation theory. With the sensitivities and covariance data of nuclear data, uncertainties of NDs of these nuclides are quantified with the JENDL libraries and others. The uncertainties of Ce-144, Cs-137 and Ru-106 are less than 2%, and that of Sb-125 is around 6%. In these uncertainties, fission yields uncertainties are dominant. On the Cs-134 and Eu-154 generations, total uncertainties are around 5% and uncertainties of (n,γ) cross sections are dominant. Those calculations are carried out with BWR pincell models, but it is also confirmed that results obtained with a BWR fuel assembly model are quite similar to those in the pincell models.

show abstract

Section: Sensitivity Calculations With the Depletion Perturbation Theorymentioning

confidence: 99%

Sensitivity and uncertainty analyses of fission product nuclide inventories for passive gamma spectroscopy

Chiba

Honta

2020

Journal of Nuclear Science and Technology

Self Cite

View full text Add to dashboard Cite

show abstract

“…Nuclides depletion equation is solved by the matrix exponential method, and the minimax polynomial approximation method is used to calculate the matrix exponential [11].…”

Section: Numerical Proceduresmentioning

confidence: 99%

Uncertainty quantification of neutron multiplication factors of light water reactor fuels during depletion

Chiba

Okumura

2018

Journal of Nuclear Science and Technology

Self Cite

View full text Add to dashboard Cite

Nuclear data-induced uncertainties of infinite neutron multiplication factors (k ∞) during fuel depletion are quantified in a single cell and a 3×3 multi-cell including burnable absorbers. Uncertainties of reaction cross sections, fission yields, decay half-lives and decay branching ratios provided in the JENDL libraries are taken into account. 100% uncertainties are assumed to nuclear data to which uncertainty information are not provided in JENDL. Uncertainties propagation calculations are carried out with the adjoint-based procedure, and required sensitivity profiles of k ∞ with respect to these nuclear data are efficiently calculated by the depletion perturbation theory. Covariance matrices for fission yields and decay data in a simplified burnup chain are successfully generated by the stochastic-based procedure. k ∞ uncertainties of about 0.6% during fuel depletion are obtained, and it is shown that actinoids reaction cross sections are dominant contributors. Nuclide-wise decomposition of the uncertainties and observation of component-wise sensitivity profiles provide physical interpretations. By virtue of the adjoint-based procedure, several parametric surveys are also conducted. Contributions of uncertainties in fission products (FP) nuclides are quantified, and important nuclides and energy ranges are identified for further evaluation of nuclear data of FP nuclides. Effect of cooling period on k ∞ uncertainties is also discussed.

show abstract

“…The Mini-Max Polynomial Approximation (MMPA) method was developed by Yosuke Kawamoto [12] as an alternative to CRAM for solving the Bateman equations. While this method is not as widely adopted as CRAM, it was also implemented in MAMMOTH to serve as a way to verify the results of CRAM.…”

Section: Mini-max Polynomial Approximation Methodsmentioning

confidence: 99%

Architecture for the Performance of Nuclear Fuel Depletion Calculations

Calvin

DeHart

2019

View full text Add to dashboard Cite

Computational analysis of the depletion of nuclear fuel is crucial to the accurate modeling of the time-dependent behavior of nuclear reactors. The reactor physics application MAMMOTH is modified to compute radioactive decay and neutron transmutation in order to model physical processes which occur within nuclear reactors as reactor fuel is burned. The ability to read decay and cross-section data files of other codes are also added and the addition of a standardized decay and transmutation XML file format for MAMMOTH, known as ISOXML. Comparisons between MAMMOTH and the Oak Ridge Isotope Generation (ORIGEN) code are performed to demonstrate the improved precision possible with MAMMOTH. In addition, several tests are run to demonstrate the ability of MAMMOTH to model decay and transmutation processes involving hundreds of isotopes. Future work will focus on solving depletion problems with multiple neutron energy groups and the implementation of predictor-corrector methods, several of which are described in this work.

show abstract

Numerical solution of matrix exponential in burn-up equation using mini-max polynomial approximation

Cited by 30 publications

References 7 publications

Sensitivity and uncertainty analyses of fission product nuclide inventories for passive gamma spectroscopy

Sensitivity and uncertainty analyses of fission product nuclide inventories for passive gamma spectroscopy

Uncertainty quantification of neutron multiplication factors of light water reactor fuels during depletion

Architecture for the Performance of Nuclear Fuel Depletion Calculations

Contact Info

Product

Resources

About