ANALYTICAL REPRESENTATION OF THE SOLUTION OF THE SPACE KINETIC DIFFUSION EQUATION IN A ONE-DIMENSIONAL AND HOMOGENEOUS DOMAIN
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional do IEN |
Texto Completo: | http://carpedien.ien.gov.br:8080/handle/ien/2144 |
Resumo: | In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron ux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modi ed decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satis ed by the recursion initialization, while from the rst recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution. |
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TUMELERO, FernandaLAPA, Celso Marcelo FranklinBODMANN, Bardo E. J.VILHENA, Marco T.Programa de Pós Graduação em Engenharia Mecânica (PROMEC) Universidade Federal do Rio Grande do SulInstituto de Engenharia Nuclear, CNEN.Programa de Pós Graduação em Engenharia Mecânica (PROMEC) Universidade Federal do Rio Grande do SulPrograma de Pós Graduação em Engenharia Mecânica (PROMEC) Universidade Federal do Rio Grande do Sul2018-01-18T18:28:00Z2018-01-18T18:28:00Zhttp://carpedien.ien.gov.br:8080/handle/ien/2144Submitted by Vanessa Silva (vanessacapucho.uerj@gmail.com) on 2018-01-18T18:28:00Z No. of bitstreams: 1 ARTIGO INAC 1.pdf: 282101 bytes, checksum: a9027370ee3e5d42dfdb21e4403992f0 (MD5)Made available in DSpace on 2018-01-18T18:28:00Z (GMT). No. of bitstreams: 1 ARTIGO INAC 1.pdf: 282101 bytes, checksum: a9027370ee3e5d42dfdb21e4403992f0 (MD5)In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron ux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modi ed decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satis ed by the recursion initialization, while from the rst recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution.engInstituto de Engenharia NuclearIENBrasilHOMOGENEOUS DOMAINANALYTICAL REPRESENTATION OF THE SOLUTION OF THE SPACE KINETIC DIFFUSION EQUATION IN A ONE-DIMENSIONAL AND HOMOGENEOUS DOMAINinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional do IENinstname:Instituto de Engenharia Nuclearinstacron:IENLICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://carpedien.ien.gov.br:8080/xmlui/bitstream/ien/2144/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52ORIGINALARTIGO INAC 1.pdfARTIGO INAC 1.pdfapplication/pdf282101http://carpedien.ien.gov.br:8080/xmlui/bitstream/ien/2144/1/ARTIGO+INAC+1.pdfa9027370ee3e5d42dfdb21e4403992f0MD51ien/2144oai:carpedien.ien.gov.br:ien/21442018-01-18 16:29:16.717Dspace IENlsales@ien.gov.brTk9URTogUExBQ0UgWU9VUiBPV04gTElDRU5TRSBIRVJFClRoaXMgc2FtcGxlIGxpY2Vuc2UgaXMgcHJvdmlkZWQgZm9yIGluZm9ybWF0aW9uYWwgcHVycG9zZXMgb25seS4KCk5PTi1FWENMVVNJVkUgRElTVFJJQlVUSU9OIExJQ0VOU0UKCkJ5IHNpZ25pbmcgYW5kIHN1Ym1pdHRpbmcgdGhpcyBsaWNlbnNlLCB5b3UgKHRoZSBhdXRob3Iocykgb3IgY29weXJpZ2h0Cm93bmVyKSBncmFudHMgdG8gRFNwYWNlIFVuaXZlcnNpdHkgKERTVSkgdGhlIG5vbi1leGNsdXNpdmUgcmlnaHQgdG8gcmVwcm9kdWNlLAp0cmFuc2xhdGUgKGFzIGRlZmluZWQgYmVsb3cpLCBhbmQvb3IgZGlzdHJpYnV0ZSB5b3VyIHN1Ym1pc3Npb24gKGluY2x1ZGluZwp0aGUgYWJzdHJhY3QpIHdvcmxkd2lkZSBpbiBwcmludCBhbmQgZWxlY3Ryb25pYyBmb3JtYXQgYW5kIGluIGFueSBtZWRpdW0sCmluY2x1ZGluZyBidXQgbm90IGxpbWl0ZWQgdG8gYXVkaW8gb3IgdmlkZW8uCgpZb3UgYWdyZWUgdGhhdCBEU1UgbWF5LCB3aXRob3V0IGNoYW5naW5nIHRoZSBjb250ZW50LCB0cmFuc2xhdGUgdGhlCnN1Ym1pc3Npb24gdG8gYW55IG1lZGl1bSBvciBmb3JtYXQgZm9yIHRoZSBwdXJwb3NlIG9mIHByZXNlcnZhdGlvbi4KCllvdSBhbHNvIGFncmVlIHRoYXQgRFNVIG1heSBrZWVwIG1vcmUgdGhhbiBvbmUgY29weSBvZiB0aGlzIHN1Ym1pc3Npb24gZm9yCnB1cnBvc2VzIG9mIHNlY3VyaXR5LCBiYWNrLXVwIGFuZCBwcmVzZXJ2YXRpb24uCgpZb3UgcmVwcmVzZW50IHRoYXQgdGhlIHN1Ym1pc3Npb24gaXMgeW91ciBvcmlnaW5hbCB3b3JrLCBhbmQgdGhhdCB5b3UgaGF2ZQp0aGUgcmlnaHQgdG8gZ3JhbnQgdGhlIHJpZ2h0cyBjb250YWluZWQgaW4gdGhpcyBsaWNlbnNlLiBZb3UgYWxzbyByZXByZXNlbnQKdGhhdCB5b3VyIHN1Ym1pc3Npb24gZG9lcyBub3QsIHRvIHRoZSBiZXN0IG9mIHlvdXIga25vd2xlZGdlLCBpbmZyaW5nZSB1cG9uCmFueW9uZSdzIGNvcHlyaWdodC4KCklmIHRoZSBzdWJtaXNzaW9uIGNvbnRhaW5zIG1hdGVyaWFsIGZvciB3aGljaCB5b3UgZG8gbm90IGhvbGQgY29weXJpZ2h0LAp5b3UgcmVwcmVzZW50IHRoYXQgeW91IGhhdmUgb2J0YWluZWQgdGhlIHVucmVzdHJpY3RlZCBwZXJtaXNzaW9uIG9mIHRoZQpjb3B5cmlnaHQgb3duZXIgdG8gZ3JhbnQgRFNVIHRoZSByaWdodHMgcmVxdWlyZWQgYnkgdGhpcyBsaWNlbnNlLCBhbmQgdGhhdApzdWNoIHRoaXJkLXBhcnR5IG93bmVkIG1hdGVyaWFsIGlzIGNsZWFybHkgaWRlbnRpZmllZCBhbmQgYWNrbm93bGVkZ2VkCndpdGhpbiB0aGUgdGV4dCBvciBjb250ZW50IG9mIHRoZSBzdWJtaXNzaW9uLgoKSUYgVEhFIFNVQk1JU1NJT04gSVMgQkFTRUQgVVBPTiBXT1JLIFRIQVQgSEFTIEJFRU4gU1BPTlNPUkVEIE9SIFNVUFBPUlRFRApCWSBBTiBBR0VOQ1kgT1IgT1JHQU5JWkFUSU9OIE9USEVSIFRIQU4gRFNVLCBZT1UgUkVQUkVTRU5UIFRIQVQgWU9VIEhBVkUKRlVMRklMTEVEIEFOWSBSSUdIVCBPRiBSRVZJRVcgT1IgT1RIRVIgT0JMSUdBVElPTlMgUkVRVUlSRUQgQlkgU1VDSApDT05UUkFDVCBPUiBBR1JFRU1FTlQuCgpEU1Ugd2lsbCBjbGVhcmx5IGlkZW50aWZ5IHlvdXIgbmFtZShzKSBhcyB0aGUgYXV0aG9yKHMpIG9yIG93bmVyKHMpIG9mIHRoZQpzdWJtaXNzaW9uLCBhbmQgd2lsbCBub3QgbWFrZSBhbnkgYWx0ZXJhdGlvbiwgb3RoZXIgdGhhbiBhcyBhbGxvd2VkIGJ5IHRoaXMKbGljZW5zZSwgdG8geW91ciBzdWJtaXNzaW9uLgo= |
dc.title.pt_BR.fl_str_mv |
ANALYTICAL REPRESENTATION OF THE SOLUTION OF THE SPACE KINETIC DIFFUSION EQUATION IN A ONE-DIMENSIONAL AND HOMOGENEOUS DOMAIN |
title |
ANALYTICAL REPRESENTATION OF THE SOLUTION OF THE SPACE KINETIC DIFFUSION EQUATION IN A ONE-DIMENSIONAL AND HOMOGENEOUS DOMAIN |
spellingShingle |
ANALYTICAL REPRESENTATION OF THE SOLUTION OF THE SPACE KINETIC DIFFUSION EQUATION IN A ONE-DIMENSIONAL AND HOMOGENEOUS DOMAIN TUMELERO, Fernanda HOMOGENEOUS DOMAIN |
title_short |
ANALYTICAL REPRESENTATION OF THE SOLUTION OF THE SPACE KINETIC DIFFUSION EQUATION IN A ONE-DIMENSIONAL AND HOMOGENEOUS DOMAIN |
title_full |
ANALYTICAL REPRESENTATION OF THE SOLUTION OF THE SPACE KINETIC DIFFUSION EQUATION IN A ONE-DIMENSIONAL AND HOMOGENEOUS DOMAIN |
title_fullStr |
ANALYTICAL REPRESENTATION OF THE SOLUTION OF THE SPACE KINETIC DIFFUSION EQUATION IN A ONE-DIMENSIONAL AND HOMOGENEOUS DOMAIN |
title_full_unstemmed |
ANALYTICAL REPRESENTATION OF THE SOLUTION OF THE SPACE KINETIC DIFFUSION EQUATION IN A ONE-DIMENSIONAL AND HOMOGENEOUS DOMAIN |
title_sort |
ANALYTICAL REPRESENTATION OF THE SOLUTION OF THE SPACE KINETIC DIFFUSION EQUATION IN A ONE-DIMENSIONAL AND HOMOGENEOUS DOMAIN |
author |
TUMELERO, Fernanda |
author_facet |
TUMELERO, Fernanda LAPA, Celso Marcelo Franklin BODMANN, Bardo E. J. VILHENA, Marco T. Programa de Pós Graduação em Engenharia Mecânica (PROMEC) Universidade Federal do Rio Grande do Sul Instituto de Engenharia Nuclear, CNEN. |
author_role |
author |
author2 |
LAPA, Celso Marcelo Franklin BODMANN, Bardo E. J. VILHENA, Marco T. Programa de Pós Graduação em Engenharia Mecânica (PROMEC) Universidade Federal do Rio Grande do Sul Instituto de Engenharia Nuclear, CNEN. |
author2_role |
author author author author author |
dc.contributor.author.fl_str_mv |
TUMELERO, Fernanda LAPA, Celso Marcelo Franklin BODMANN, Bardo E. J. VILHENA, Marco T. Programa de Pós Graduação em Engenharia Mecânica (PROMEC) Universidade Federal do Rio Grande do Sul Instituto de Engenharia Nuclear, CNEN. Programa de Pós Graduação em Engenharia Mecânica (PROMEC) Universidade Federal do Rio Grande do Sul Programa de Pós Graduação em Engenharia Mecânica (PROMEC) Universidade Federal do Rio Grande do Sul |
dc.subject.por.fl_str_mv |
HOMOGENEOUS DOMAIN |
topic |
HOMOGENEOUS DOMAIN |
dc.description.abstract.por.fl_txt_mv |
In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron ux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modi ed decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satis ed by the recursion initialization, while from the rst recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution. |
description |
In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron ux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modi ed decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satis ed by the recursion initialization, while from the rst recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution. |
publishDate |
2018 |
dc.date.accessioned.fl_str_mv |
2018-01-18T18:28:00Z |
dc.date.available.fl_str_mv |
2018-01-18T18:28:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
status_str |
publishedVersion |
format |
article |
dc.identifier.uri.fl_str_mv |
http://carpedien.ien.gov.br:8080/handle/ien/2144 |
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http://carpedien.ien.gov.br:8080/handle/ien/2144 |
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eng |
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eng |
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openAccess |
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Instituto de Engenharia Nuclear |
dc.publisher.initials.fl_str_mv |
IEN |
dc.publisher.country.fl_str_mv |
Brasil |
publisher.none.fl_str_mv |
Instituto de Engenharia Nuclear |
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reponame:Repositório Institucional do IEN instname:Instituto de Engenharia Nuclear instacron:IEN |
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Repositório Institucional do IEN |
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Repositório Institucional do IEN |
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IEN |
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IEN |
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