{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/74794"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/74794","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"An efficient method for the solution of the energy dependent integral Boltzmann transport equation in the resolved resonance energy region","abstract":"The calculation of neutron-nuclei reaction rates in the lower resolved resonance region (167 ev - l.855 ev) is considered in this dissertation. Particular emphasis is placed on the calculation of these reaction rates for tight lattices where their accuracy is most important. The results of the continuous energy Monte Carlo code, VIM, are chosen as reference values for this study. The primary objective of this work is to develop a method for calculating resonance reaction rates which agrees well with the reference solution, yet is efficient enough to be used by nuclear reactor fuel cycle designers on a production basis. A very efficient multigroup solution of the two spatial region energy dependent integral transport equation is developed. This solution, denoted the \"Broad Group Integral Method'' (BGIM), uses escape probabilities to obtain the spatial coupling between regions and uses an analytical flux shape within a multigroup to obtain weighted cross sections which account for the rapidly varying resonance cross sections. The multigroup lethargy widths chosen for the numerical integration of the two region energy-dependent neutron continuity equations can be chosen much wider (a factor of 30 larger) than in the direct numerical integration methods since the analytical f1ux shape is used to account for fine structure effects. The BGIM solution is made highly efficient through the use of these broad groups. It is estimated that for a 10 step unit cell fuel cycle depletion calculation, the computer running time for a production code such as EPRI-LEOPARD would be increased by only 6% through the use of the more accurate and intricate BGIM method in the lower resonance energy region. A comprehensive numerical verification of the proposed method is performed. Numerous comparisons are made to VIM for an infinite repeating lattice. These comparisons consider isotopic changes caused by burnup and enrichment variations, cold and hot temperatures in fuel and moderator, and lattice geometry variations. These results show the \"Broad Group Integral Method\" (BGIM) to be an efficient and accurate solution of the Energy dependent integral Boltzmann transport equation in the resolved resonance energy region.","abstract_html":"The calculation of neutron-nuclei reaction rates in the lower resolved resonance region (167 ev - l.855 ev) is considered in this dissertation. Particular emphasis is placed on the calculation of these reaction rates for tight lattices where their accuracy is most important. The results of the continuous energy Monte Carlo code, VIM, are chosen as reference values for this study. The primary objective of this work is to develop a method for calculating resonance reaction rates which agrees well with the reference solution, yet is efficient enough to be used by nuclear reactor fuel cycle designers on a production basis. A very efficient multigroup solution of the two spatial region energy dependent integral transport equation is developed. This solution, denoted the "Broad Group Integral Method'' (BGIM), uses escape probabilities to obtain the spatial coupling between regions and uses an analytical flux shape within a multigroup to obtain weighted cross sections which account for the rapidly varying resonance cross sections. The multigroup lethargy widths chosen for the numerical integration of the two region energy-dependent neutron continuity equations can be chosen much wider (a factor of 30 larger) than in the direct numerical integration methods since the analytical f1ux shape is used to account for fine structure effects. The BGIM solution is made highly efficient through the use of these broad groups. It is estimated that for a 10 step unit cell fuel cycle depletion calculation, the computer running time for a production code such as EPRI-LEOPARD would be increased by only 6% through the use of the more accurate and intricate BGIM method in the lower resonance energy region. A comprehensive numerical verification of the proposed method is performed. Numerous comparisons are made to VIM for an infinite repeating lattice. These comparisons consider isotopic changes caused by burnup and enrichment variations, cold and hot temperatures in fuel and moderator, and lattice geometry variations. These results show the "Broad Group Integral Method" (BGIM) to be an efficient and accurate solution of the Energy dependent integral Boltzmann transport equation in the resolved resonance energy region.","abstract_has_math":false,"creators":["Schwenk, George Arthur"],"institution":"Virginia Polytechnic Institute and State University","degree_name":"Ph. D.","degree_level":"doctoral","degree_discipline":"Nuclear Science and Engineering","degree_department":"Nuclear Science and Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1980,"date_issued":"1980","date_published":"1980","updated_at":"2026-07-22T22:20:31Z","subjects":[],"languages":["en_US"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10919/74794","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Nuclear Science and Engineering"]},{"key":"dc:creator","label":"Author","values":["Schwenk, George Arthur"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-01-30T21:24:48Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-01-30T21:24:48Z"]},{"key":"dc:date.issued","label":"Date","values":["1980"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Polytechnic Institute and State University"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Nuclear Science and Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. 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The results of the continuous energy Monte Carlo code, VIM, are chosen as reference values for this study. The primary objective of this work is to develop a method for calculating resonance reaction rates which agrees well with the reference solution, yet is efficient enough to be used by nuclear reactor fuel cycle designers on a production basis. A very efficient multigroup solution of the two spatial region energy dependent integral transport equation is developed. This solution, denoted the \"Broad Group Integral Method'' (BGIM), uses escape probabilities to obtain the spatial coupling between regions and uses an analytical flux shape within a multigroup to obtain weighted cross sections which account for the rapidly varying resonance cross sections. The multigroup lethargy widths chosen for the numerical integration of the two region energy-dependent neutron continuity equations can be chosen much wider (a factor of 30 larger) than in the direct numerical integration methods since the analytical f1ux shape is used to account for fine structure effects. The BGIM solution is made highly efficient through the use of these broad groups. It is estimated that for a 10 step unit cell fuel cycle depletion calculation, the computer running time for a production code such as EPRI-LEOPARD would be increased by only 6% through the use of the more accurate and intricate BGIM method in the lower resonance energy region. A comprehensive numerical verification of the proposed method is performed. Numerous comparisons are made to VIM for an infinite repeating lattice. These comparisons consider isotopic changes caused by burnup and enrichment variations, cold and hot temperatures in fuel and moderator, and lattice geometry variations. These results show the \"Broad Group Integral Method\" (BGIM) to be an efficient and accurate solution of the Energy dependent integral Boltzmann transport equation in the resolved resonance energy region."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["An efficient method for the solution of the energy dependent integral Boltzmann transport equation in the resolved resonance energy region"]}]}],"canonical_facts":{"dc:contributor.department":["Nuclear Science and Engineering"],"dc:creator":["Schwenk, George Arthur"],"dc:date.accessioned":["2017-01-30T21:24:48Z"],"dc:date.available":["2017-01-30T21:24:48Z"],"dc:date.issued":["1980"],"dc:description.abstract":["The calculation of neutron-nuclei reaction rates in the lower resolved resonance region (167 ev - l.855 ev) is considered in this dissertation. Particular emphasis is placed on the calculation of these reaction rates for tight lattices where their accuracy is most important. The results of the continuous energy Monte Carlo code, VIM, are chosen as reference values for this study. The primary objective of this work is to develop a method for calculating resonance reaction rates which agrees well with the reference solution, yet is efficient enough to be used by nuclear reactor fuel cycle designers on a production basis. A very efficient multigroup solution of the two spatial region energy dependent integral transport equation is developed. This solution, denoted the \"Broad Group Integral Method'' (BGIM), uses escape probabilities to obtain the spatial coupling between regions and uses an analytical flux shape within a multigroup to obtain weighted cross sections which account for the rapidly varying resonance cross sections. The multigroup lethargy widths chosen for the numerical integration of the two region energy-dependent neutron continuity equations can be chosen much wider (a factor of 30 larger) than in the direct numerical integration methods since the analytical f1ux shape is used to account for fine structure effects. The BGIM solution is made highly efficient through the use of these broad groups. It is estimated that for a 10 step unit cell fuel cycle depletion calculation, the computer running time for a production code such as EPRI-LEOPARD would be increased by only 6% through the use of the more accurate and intricate BGIM method in the lower resonance energy region. A comprehensive numerical verification of the proposed method is performed. Numerous comparisons are made to VIM for an infinite repeating lattice. These comparisons consider isotopic changes caused by burnup and enrichment variations, cold and hot temperatures in fuel and moderator, and lattice geometry variations. These results show the \"Broad Group Integral Method\" (BGIM) to be an efficient and accurate solution of the Energy dependent integral Boltzmann transport equation in the resolved resonance energy region."],"dc:description.degree":["Ph. D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/74794"],"dc:language.iso":["en_US"],"dc:publisher":["Virginia Polytechnic Institute and State University"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["An efficient method for the solution of the energy dependent integral Boltzmann transport equation in the resolved resonance energy region"],"dc:type":["Dissertation"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Nuclear Science and Engineering"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:31Z"}