{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/20972"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/20972","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Computational simulation of buoyancy-driven flows using vortex methods","abstract":"A new vortex method for simulating two-dimensional buoyancy-driven flows is presented. This Lagrangian method utilizes a discrete representation of the known density field along with the vorticity transport equation and Boussinesq approximation to yield the baroclinically-generated vorticity field, also in a discrete form. The corresponding velocity field is then computed using a vorticity-streamfunction scheme similar to the vortex-in-cell approach. Complete simulations for a variety of Rayleigh-Taylor stability problems are presented, as are preliminary results for Rayleigh-Bernard flows.","abstract_html":"A new vortex method for simulating two-dimensional buoyancy-driven flows is presented. This Lagrangian method utilizes a discrete representation of the known density field along with the vorticity transport equation and Boussinesq approximation to yield the baroclinically-generated vorticity field, also in a discrete form. The corresponding velocity field is then computed using a vorticity-streamfunction scheme similar to the vortex-in-cell approach. Complete simulations for a variety of Rayleigh-Taylor stability problems are presented, as are preliminary results for Rayleigh-Bernard flows.","abstract_has_math":false,"creators":["Egan, Erik Witmer"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Chemical Engineering","degree_department":null,"school":null,"contributors":["Higdon, Jonathan J.L."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:54:36Z","date_published":"2011-05-07T12:54:36Z","updated_at":"2026-07-22T22:25:17Z","subjects":["Engineering, Chemical","Physics, Fluid and Plasma"],"languages":["eng"],"rights":["Copyright 1989 Egan, Erik Witmer"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI8924811","(UMI)AAI8924811"],"render_values":[{"text":"AAI8924811","href":null,"code":true},{"text":"(UMI)AAI8924811","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/20972","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Higdon, Jonathan J.L."]},{"key":"dc:creator","label":"Author","values":["Egan, Erik Witmer"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:54:36Z","10000-01-01","1989"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Chemical 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, Chemical","Physics, Fluid and Plasma"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1989 Egan, Erik Witmer"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI8924811","(UMI)AAI8924811","http://hdl.handle.net/2142/20972"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A new vortex method for simulating two-dimensional buoyancy-driven flows is presented. This Lagrangian method utilizes a discrete representation of the known density field along with the vorticity transport equation and Boussinesq approximation to yield the baroclinically-generated vorticity field, also in a discrete form. The corresponding velocity field is then computed using a vorticity-streamfunction scheme similar to the vortex-in-cell approach. Complete simulations for a variety of Rayleigh-Taylor stability problems are presented, as are preliminary results for Rayleigh-Bernard flows.","The discrete vorticity field is made up of vertically-oriented vortex dipole markers. The mutual interactions among these markers are determined by redistributing the dipolar marker vorticity onto a fixed array of true vortices. Standard vortex-in-cell techniques can then be used to generate marker velocities. The vorticity redistribution step is accomplished by matching the far-field velocity of a single dipole marker to that generated by the local grid vortices. The overall simulation method is termed the Dipole-in-Cell approach. Viscous and thermal diffusion effects (for Rayleigh-Benard flows only) are described using a random walk scheme.","\"Rayleigh-Taylor simulations for both single- and double-interface geometries show the expected linear and nonlinear flow development, including the recirculation associated with the Kelvin-Helmholtz interfacial instability. The double-interface results show the development of an \"\"anti-spike\"\" along the top interface, as seen in other studies. The simulations are also shown to be capable of following the impact of a mass of fluid on solid boundaries and pools of stagnant fluid.\"","The Rayleigh-Benard results demonstrate the validity of the random walk mechanism for simulating diffusion and the ability to generate rough representations of the classic Benard convection cells. The accuracy of the Benard cell results is limited by the long computation times required to reach steady state for small Rayleigh numbers. For the large Rayleigh number flows of greatest interest, no such problems will occur and the method should be well suited to simulating them. Suggestions are made for method improvements, including extensions to three-dimensional flow problems.","Made available in DSpace on 2011-05-07T12:54:36Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8924811.pdf: 8085176 bytes, checksum: 15af7acdf0915d3a2e39888185c81c15 (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:47:37Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:21:30-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Computational simulation of buoyancy-driven flows using vortex methods"]}]}],"canonical_facts":{"dc:contributor":["Higdon, Jonathan J.L."],"dc:creator":["Egan, Erik Witmer"],"dc:date":["2011-05-07T12:54:36Z","10000-01-01","1989"],"dc:description":["A new vortex method for simulating two-dimensional buoyancy-driven flows is presented. This Lagrangian method utilizes a discrete representation of the known density field along with the vorticity transport equation and Boussinesq approximation to yield the baroclinically-generated vorticity field, also in a discrete form. The corresponding velocity field is then computed using a vorticity-streamfunction scheme similar to the vortex-in-cell approach. Complete simulations for a variety of Rayleigh-Taylor stability problems are presented, as are preliminary results for Rayleigh-Bernard flows.","The discrete vorticity field is made up of vertically-oriented vortex dipole markers. The mutual interactions among these markers are determined by redistributing the dipolar marker vorticity onto a fixed array of true vortices. Standard vortex-in-cell techniques can then be used to generate marker velocities. The vorticity redistribution step is accomplished by matching the far-field velocity of a single dipole marker to that generated by the local grid vortices. The overall simulation method is termed the Dipole-in-Cell approach. Viscous and thermal diffusion effects (for Rayleigh-Benard flows only) are described using a random walk scheme.","\"Rayleigh-Taylor simulations for both single- and double-interface geometries show the expected linear and nonlinear flow development, including the recirculation associated with the Kelvin-Helmholtz interfacial instability. The double-interface results show the development of an \"\"anti-spike\"\" along the top interface, as seen in other studies. The simulations are also shown to be capable of following the impact of a mass of fluid on solid boundaries and pools of stagnant fluid.\"","The Rayleigh-Benard results demonstrate the validity of the random walk mechanism for simulating diffusion and the ability to generate rough representations of the classic Benard convection cells. The accuracy of the Benard cell results is limited by the long computation times required to reach steady state for small Rayleigh numbers. For the large Rayleigh number flows of greatest interest, no such problems will occur and the method should be well suited to simulating them. Suggestions are made for method improvements, including extensions to three-dimensional flow problems.","Made available in DSpace on 2011-05-07T12:54:36Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8924811.pdf: 8085176 bytes, checksum: 15af7acdf0915d3a2e39888185c81c15 (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:47:37Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:21:30-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI8924811","(UMI)AAI8924811","http://hdl.handle.net/2142/20972"],"dc:language":["eng"],"dc:rights":["Copyright 1989 Egan, Erik Witmer"],"dc:subject":["Engineering, Chemical","Physics, Fluid and Plasma"],"dc:title":["Computational simulation of buoyancy-driven flows using vortex methods"],"dc:type":["text"],"thesis:degree_discipline":["Chemical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:17Z"}