Journal article Open Access

# Numerical solution of two-energy-group neutron noise diffusion problems with fine spatial meshes

Antonios G. Mylonakis; Paolo VInai; Christophe Demazière

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<identifier identifierType="URL">https://zenodo.org/record/3701600</identifier>
<creators>
<creator>
<creatorName>Antonios G. Mylonakis</creatorName>
<affiliation>Chalmers University of Technology</affiliation>
</creator>
<creator>
<creatorName>Paolo VInai</creatorName>
<affiliation>Chalmers University of Technology</affiliation>
</creator>
<creator>
<creatorName>Christophe Demazière</creatorName>
<affiliation>Chalmers University of Technology</affiliation>
</creator>
</creators>
<titles>
<title>Numerical solution of two-energy-group neutron noise diffusion problems with fine spatial meshes</title>
</titles>
<publisher>Zenodo</publisher>
<publicationYear>2020</publicationYear>
<subjects>
<subject>reactor neutron noise</subject>
<subject>k-eigenvalue problem</subject>
<subject>GMRES</subject>
<subject>nonlinear acceleration</subject>
<subject>JFNK</subject>
<subject>SPAI</subject>
</subjects>
<dates>
<date dateType="Issued">2020-06-01</date>
</dates>
<language>en</language>
<resourceType resourceTypeGeneral="Text">Journal article</resourceType>
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<alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/3701600</alternateIdentifier>
</alternateIdentifiers>
<relatedIdentifiers>
<relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1016/j.anucene.2019.107093</relatedIdentifier>
</relatedIdentifiers>
<rightsList>
<rights rightsURI="https://creativecommons.org/licenses/by/4.0/legalcode">Creative Commons Attribution 4.0 International</rights>
<rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
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<descriptions>
<description descriptionType="Abstract">&lt;p&gt;The paper presents the development of a strategy for the fine-mesh full-core computation of neutron noise in nuclear reactors. Reactor neutron noise is related to fluctuations of the neutron flux induced by stationary perturbations of the properties of the system. Its monitoring and analysis can provide useful insights in the reactor operations. The model used in the work relies on the neutron diffusion approximation and requires the solution of both the criticality (eigenvalue) and neutron noise equations. A high-resolution spatial discretization of the equations is important for an accurate evaluation of the neutron noise because of the strong gradients that may arise from the perturbations. Considering the size of a nuclear reactor, the application of a fine mesh generates large systems of equations which can be challenging to solve. Then, numerical methods that can provide efficient solutions for these kinds of problems using a reasonable computational effort, are investigated. In particular the power method accelerated with the Chebychev or JFNK-based techniques for the eigenvalue problem, and GMRES with the Symmetric Gauss-Seidel, ILU, SPAI preconditioners for the solution of linear systems, are evaluated with the computation of neutron noise in the case of localized perturbations in 1-D and 2-D simplified reactor cores and in a 3D realistic reactor core.&lt;/p&gt;</description>
</descriptions>
<fundingReferences>
<fundingReference>
<funderName>European Commission</funderName>
<funderIdentifier funderIdentifierType="Crossref Funder ID">10.13039/501100000780</funderIdentifier>
<awardNumber awardURI="info:eu-repo/grantAgreement/EC/H2020/754316/">754316</awardNumber>
<awardTitle>Core monitoring techniques and experimental validation and demonstration</awardTitle>
</fundingReference>
</fundingReferences>
</resource>

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