{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/21160"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/21160","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Simulation of time-dependent free surface Navier-Stokes flows","abstract":"\"Two numerical methods for simulation of time-dependent free-surface Navier-Stokes flows are developed. Both techniques are based on semi-implicit time advancement of the momentum equations, integral formulation of the spatial problem at each timestep, and spectral-element discretization to solve the resulting integral equation. Central to each algorithm is a boundary-specific solution step which permits the spatial treatment in two dimensions to be performed in O(N$\\sp3$) operations per timestep despite the presence of deforming geometry. The first approach is a \"\"domain-integral\"\" formulation involving integrals over the entire flow domain of kernel functions which arise in time-differencing the Navier-Stokes equations. The second is a \"\"particular-solution\"\" formulation which replaces domain integration with an iterative scheme to generate particular velocity and pressure fields on individual elements, followed by a patching step to produce a particular solution continuous over the full domain. Two of the most difficult aspects of viscous free-surface flow simulations, namely time-dependent geometry and nontrivial boundary conditions, are well accommodated by these integral equation techniques. In addition the methods offer spectral accuracy in space and admit arbitrarily high-order discretization in time. For large-scale computations and/or long-term time advancement the domain-integral algorithm must be executed on a supercomputer to deliver results in reasonable processing time. A detailed simulation of gas-liquid flow with full resolution of the free phase boundary requires approximately five CPU hours at 80 megaflops. The particular-solution formulation is faster than the domain-integral technique by a factor of eight or more, completing the same gas-liquid flow calculation in about 36 CPU minutes. Timestepping tests of the latter method are still in progress, but the algorithm shows significant potential for making high-resolution modelling of fluid flow and other transport phenomena practical in the near future.\"","abstract_html":""Two numerical methods for simulation of time-dependent free-surface Navier-Stokes flows are developed. Both techniques are based on semi-implicit time advancement of the momentum equations, integral formulation of the spatial problem at each timestep, and spectral-element discretization to solve the resulting integral equation. Central to each algorithm is a boundary-specific solution step which permits the spatial treatment in two dimensions to be performed in O(N$\\sp3$) operations per timestep despite the presence of deforming geometry. The first approach is a ""domain-integral"" formulation involving integrals over the entire flow domain of kernel functions which arise in time-differencing the Navier-Stokes equations. The second is a ""particular-solution"" formulation which replaces domain integration with an iterative scheme to generate particular velocity and pressure fields on individual elements, followed by a patching step to produce a particular solution continuous over the full domain. Two of the most difficult aspects of viscous free-surface flow simulations, namely time-dependent geometry and nontrivial boundary conditions, are well accommodated by these integral equation techniques. In addition the methods offer spectral accuracy in space and admit arbitrarily high-order discretization in time. For large-scale computations and/or long-term time advancement the domain-integral algorithm must be executed on a supercomputer to deliver results in reasonable processing time. A detailed simulation of gas-liquid flow with full resolution of the free phase boundary requires approximately five CPU hours at 80 megaflops. The particular-solution formulation is faster than the domain-integral technique by a factor of eight or more, completing the same gas-liquid flow calculation in about 36 CPU minutes. Timestepping tests of the latter method are still in progress, but the algorithm shows significant potential for making high-resolution modelling of fluid flow and other transport phenomena practical in the near future."","abstract_has_math":true,"creators":["Muldowney, Gregory Patrick"],"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":"2011-05-07T13:00:08Z","date_published":"2011-05-07T13:00:08Z","updated_at":"2026-07-22T22:25:17Z","subjects":["Engineering, Chemical"],"languages":["eng"],"rights":["Copyright 1989 Muldowney, Gregory Patrick"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI8916288","(UMI)AAI8916288"],"render_values":[{"text":"AAI8916288","href":null,"code":true},{"text":"(UMI)AAI8916288","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/21160","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":["Muldowney, Gregory Patrick"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:00:08Z","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"]}]},{"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 Muldowney, Gregory Patrick"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI8916288","(UMI)AAI8916288","http://hdl.handle.net/2142/21160"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"Two numerical methods for simulation of time-dependent free-surface Navier-Stokes flows are developed. Both techniques are based on semi-implicit time advancement of the momentum equations, integral formulation of the spatial problem at each timestep, and spectral-element discretization to solve the resulting integral equation. Central to each algorithm is a boundary-specific solution step which permits the spatial treatment in two dimensions to be performed in O(N$\\sp3$) operations per timestep despite the presence of deforming geometry. The first approach is a \"\"domain-integral\"\" formulation involving integrals over the entire flow domain of kernel functions which arise in time-differencing the Navier-Stokes equations. The second is a \"\"particular-solution\"\" formulation which replaces domain integration with an iterative scheme to generate particular velocity and pressure fields on individual elements, followed by a patching step to produce a particular solution continuous over the full domain. Two of the most difficult aspects of viscous free-surface flow simulations, namely time-dependent geometry and nontrivial boundary conditions, are well accommodated by these integral equation techniques. In addition the methods offer spectral accuracy in space and admit arbitrarily high-order discretization in time. For large-scale computations and/or long-term time advancement the domain-integral algorithm must be executed on a supercomputer to deliver results in reasonable processing time. A detailed simulation of gas-liquid flow with full resolution of the free phase boundary requires approximately five CPU hours at 80 megaflops. The particular-solution formulation is faster than the domain-integral technique by a factor of eight or more, completing the same gas-liquid flow calculation in about 36 CPU minutes. Timestepping tests of the latter method are still in progress, but the algorithm shows significant potential for making high-resolution modelling of fluid flow and other transport phenomena practical in the near future.\"","Made available in DSpace on 2011-05-07T13:00:08Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8916288.pdf: 7127225 bytes, checksum: e60d31c836400d88db68a0d9a6e377ed (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:48:53Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:22:11-05:00 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":["Simulation of time-dependent free surface Navier-Stokes flows"]}]}],"canonical_facts":{"dc:contributor":["Higdon, Jonathan J.L."],"dc:creator":["Muldowney, Gregory Patrick"],"dc:date":["2011-05-07T13:00:08Z","10000-01-01","1989"],"dc:description":["\"Two numerical methods for simulation of time-dependent free-surface Navier-Stokes flows are developed. Both techniques are based on semi-implicit time advancement of the momentum equations, integral formulation of the spatial problem at each timestep, and spectral-element discretization to solve the resulting integral equation. Central to each algorithm is a boundary-specific solution step which permits the spatial treatment in two dimensions to be performed in O(N$\\sp3$) operations per timestep despite the presence of deforming geometry. The first approach is a \"\"domain-integral\"\" formulation involving integrals over the entire flow domain of kernel functions which arise in time-differencing the Navier-Stokes equations. The second is a \"\"particular-solution\"\" formulation which replaces domain integration with an iterative scheme to generate particular velocity and pressure fields on individual elements, followed by a patching step to produce a particular solution continuous over the full domain. Two of the most difficult aspects of viscous free-surface flow simulations, namely time-dependent geometry and nontrivial boundary conditions, are well accommodated by these integral equation techniques. In addition the methods offer spectral accuracy in space and admit arbitrarily high-order discretization in time. For large-scale computations and/or long-term time advancement the domain-integral algorithm must be executed on a supercomputer to deliver results in reasonable processing time. A detailed simulation of gas-liquid flow with full resolution of the free phase boundary requires approximately five CPU hours at 80 megaflops. The particular-solution formulation is faster than the domain-integral technique by a factor of eight or more, completing the same gas-liquid flow calculation in about 36 CPU minutes. Timestepping tests of the latter method are still in progress, but the algorithm shows significant potential for making high-resolution modelling of fluid flow and other transport phenomena practical in the near future.\"","Made available in DSpace on 2011-05-07T13:00:08Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8916288.pdf: 7127225 bytes, checksum: e60d31c836400d88db68a0d9a6e377ed (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:48:53Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:22:11-05:00 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":["AAI8916288","(UMI)AAI8916288","http://hdl.handle.net/2142/21160"],"dc:language":["eng"],"dc:rights":["Copyright 1989 Muldowney, Gregory Patrick"],"dc:subject":["Engineering, Chemical"],"dc:title":["Simulation of time-dependent free surface Navier-Stokes flows"],"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"}