{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/72241"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/72241","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"An Adaptive Mesh Refinement Scheme for Solidification Problems","abstract":"Methods for adaptive mesh refinement, based on a quadtree data structure, have been developed with the specific objective of tracking a solid/liquid front in a two-dimensional solidification problem. These methods include mesh refinement and unrefinement algorithms for the finite element method applied to transient problems. An a posteriori error estimator is described to locate regions in the finite element mesh needing refinement. Implementation of the methods to work in conjunction with FIDAP$\\sp{\\rm TM}$ and TOPAZ2D$\\sp{\\copyright}$ are presented. One- and two-dimensional examples of applications are given, showing how the methods can be used to resolve the solidification front. These methods have been used to solve the temperature and concentration fields for binary alloy solidification. Formulations and solution schemes for these problems have been described.","abstract_html":"Methods for adaptive mesh refinement, based on a quadtree data structure, have been developed with the specific objective of tracking a solid/liquid front in a two-dimensional solidification problem. These methods include mesh refinement and unrefinement algorithms for the finite element method applied to transient problems. An a posteriori error estimator is described to locate regions in the finite element mesh needing refinement. Implementation of the methods to work in conjunction with FIDAP$\\sp{\\rm TM}$ and TOPAZ2D$\\sp{\\copyright}$ are presented. One- and two-dimensional examples of applications are given, showing how the methods can be used to resolve the solidification front. These methods have been used to solve the temperature and concentration fields for binary alloy solidification. Formulations and solution schemes for these problems have been described.","abstract_has_math":true,"creators":["Palle, Nagendra"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Dantzig, Jonathan A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-17T21:26:18Z","date_published":"2014-12-17T21:26:18Z","updated_at":"2026-07-22T22:26:06Z","subjects":["Engineering, Mechanical","Engineering, Materials Science","Engineering, Civil"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI9411743"],"render_values":[{"text":"(UMI)AAI9411743","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/72241","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dantzig, Jonathan A."]},{"key":"dc:creator","label":"Author","values":["Palle, Nagendra"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-17T21:26:18Z","10000-01-01","1993"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Mechanical","Engineering, Materials Science","Engineering, Civil"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/72241","(UMI)AAI9411743"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Methods for adaptive mesh refinement, based on a quadtree data structure, have been developed with the specific objective of tracking a solid/liquid front in a two-dimensional solidification problem. These methods include mesh refinement and unrefinement algorithms for the finite element method applied to transient problems. An a posteriori error estimator is described to locate regions in the finite element mesh needing refinement. Implementation of the methods to work in conjunction with FIDAP$\\sp{\\rm TM}$ and TOPAZ2D$\\sp{\\copyright}$ are presented. One- and two-dimensional examples of applications are given, showing how the methods can be used to resolve the solidification front. These methods have been used to solve the temperature and concentration fields for binary alloy solidification. Formulations and solution schemes for these problems have been described.","Made available in DSpace on 2014-12-17T21:26:18Z (GMT). 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These methods include mesh refinement and unrefinement algorithms for the finite element method applied to transient problems. An a posteriori error estimator is described to locate regions in the finite element mesh needing refinement. Implementation of the methods to work in conjunction with FIDAP$\\sp{\\rm TM}$ and TOPAZ2D$\\sp{\\copyright}$ are presented. One- and two-dimensional examples of applications are given, showing how the methods can be used to resolve the solidification front. These methods have been used to solve the temperature and concentration fields for binary alloy solidification. Formulations and solution schemes for these problems have been described.","Made available in DSpace on 2014-12-17T21:26:18Z (GMT). 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