{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/106470"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/106470","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Variational multiscale method for coupled systems: free-surface flows and stratified turbulence","abstract":"This dissertation presents a robust numerical method for the class of coupled systems comprised of multiple interacting partial differential equations (PDE). Particular emphasis is placed on incompressible Navier-Stokes equations that are coupled with a hyperbolic scalar PDE. The method is derived based on the variational multiscale (VMS) framework. Specifically, two classes of coupled systems are considered: free-surface flows with a sharp interface marker and stratified turbulence with a smooth temperature field. The additional nonlinearity introduced by the active scalar field to the nonlinear Navier-Stokes equation system is effectively accounted for by variationally derived stabilization term. In the context of the free-surface flows that are modeled by immiscible two-phase fluids, the dependency of fluid mechanical properties (i.e., density and viscosity) on the implicit interface marker (e.g., signed distance field) results in an interface that traverses through the elements. Applying VMS method to the coupled system results in an interface stabilization term. It is shown that the structure of the stabilization term leads to the so-called Ghost-Penalty method. In the context of internal dissipation in thermodynamics for incompressible flow with Boussinesq approximation, an energy conservation equation is appended that gives rise to a thermomechanically coupled system. The coupled fine-scale sub-problem is locally resolved to yield the closure model. The fine-scale turbulence features are accounted for by the VMS strategy wherein the hierarchical application of VMS results in further enhancement of the mass conservation. The new method for coupled systems is implemented using hexahedral and tetrahedral elements, and the code is parallelized for the distributed memory system. A range of problems is presented to show the mathematical and computational features of the method.","abstract_html":"This dissertation presents a robust numerical method for the class of coupled systems comprised of multiple interacting partial differential equations (PDE). Particular emphasis is placed on incompressible Navier-Stokes equations that are coupled with a hyperbolic scalar PDE. The method is derived based on the variational multiscale (VMS) framework. Specifically, two classes of coupled systems are considered: free-surface flows with a sharp interface marker and stratified turbulence with a smooth temperature field. The additional nonlinearity introduced by the active scalar field to the nonlinear Navier-Stokes equation system is effectively accounted for by variationally derived stabilization term. In the context of the free-surface flows that are modeled by immiscible two-phase fluids, the dependency of fluid mechanical properties (i.e., density and viscosity) on the implicit interface marker (e.g., signed distance field) results in an interface that traverses through the elements. Applying VMS method to the coupled system results in an interface stabilization term. It is shown that the structure of the stabilization term leads to the so-called Ghost-Penalty method. In the context of internal dissipation in thermodynamics for incompressible flow with Boussinesq approximation, an energy conservation equation is appended that gives rise to a thermomechanically coupled system. The coupled fine-scale sub-problem is locally resolved to yield the closure model. The fine-scale turbulence features are accounted for by the VMS strategy wherein the hierarchical application of VMS results in further enhancement of the mass conservation. The new method for coupled systems is implemented using hexahedral and tetrahedral elements, and the code is parallelized for the distributed memory system. A range of problems is presented to show the mathematical and computational features of the method.","abstract_has_math":false,"creators":["Zhu, Lixing"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Civil Engineering","degree_department":null,"school":null,"contributors":["Masud, Arif","Duarte, C. Armando","Lopez-Pamies, Oscar","Yan, Jinhui"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-03-02T22:38:49Z","date_published":"2020-03-02T22:38:49Z","updated_at":"2026-07-22T22:24:47Z","subjects":["Turbulent modelling","Variational Multiscale method","Arbitrary Lagrangian-Eulerian","Level-set method","Stratification","Free surfaces","Interface stabilization"],"languages":["en"],"rights":["Copyright 2019 Lixing Zhu"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/106470","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Masud, Arif","Duarte, C. 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Particular emphasis is placed on incompressible Navier-Stokes equations that are coupled with a hyperbolic scalar PDE. The method is derived based on the variational multiscale (VMS) framework. Specifically, two classes of coupled systems are considered: free-surface flows with a sharp interface marker and stratified turbulence with a smooth temperature field. The additional nonlinearity introduced by the active scalar field to the nonlinear Navier-Stokes equation system is effectively accounted for by variationally derived stabilization term. In the context of the free-surface flows that are modeled by immiscible two-phase fluids, the dependency of fluid mechanical properties (i.e., density and viscosity) on the implicit interface marker (e.g., signed distance field) results in an interface that traverses through the elements. Applying VMS method to the coupled system results in an interface stabilization term. It is shown that the structure of the stabilization term leads to the so-called Ghost-Penalty method. In the context of internal dissipation in thermodynamics for incompressible flow with Boussinesq approximation, an energy conservation equation is appended that gives rise to a thermomechanically coupled system. The coupled fine-scale sub-problem is locally resolved to yield the closure model. The fine-scale turbulence features are accounted for by the VMS strategy wherein the hierarchical application of VMS results in further enhancement of the mass conservation. The new method for coupled systems is implemented using hexahedral and tetrahedral elements, and the code is parallelized for the distributed memory system. A range of problems is presented to show the mathematical and computational features of the method.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2021-12-01","The student, Lixing Zhu, accepted the attached license on 2019-12-02 at 15:46.","The student, Lixing Zhu, submitted this Dissertation for approval on 2019-12-02 at 17:53.","This Dissertation was approved for publication on 2019-12-04 at 08:50.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14647 on 2020-02-28 at 17:37:08","Made available in DSpace on 2020-03-02T22:38:49Z (GMT). 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Armando","Lopez-Pamies, Oscar","Yan, Jinhui"],"dc:creator":["Zhu, Lixing"],"dc:date":["2020-03-02T22:38:49Z","2019-12-04","2019-12"],"dc:description":["This dissertation presents a robust numerical method for the class of coupled systems comprised of multiple interacting partial differential equations (PDE). Particular emphasis is placed on incompressible Navier-Stokes equations that are coupled with a hyperbolic scalar PDE. The method is derived based on the variational multiscale (VMS) framework. Specifically, two classes of coupled systems are considered: free-surface flows with a sharp interface marker and stratified turbulence with a smooth temperature field. The additional nonlinearity introduced by the active scalar field to the nonlinear Navier-Stokes equation system is effectively accounted for by variationally derived stabilization term. In the context of the free-surface flows that are modeled by immiscible two-phase fluids, the dependency of fluid mechanical properties (i.e., density and viscosity) on the implicit interface marker (e.g., signed distance field) results in an interface that traverses through the elements. Applying VMS method to the coupled system results in an interface stabilization term. It is shown that the structure of the stabilization term leads to the so-called Ghost-Penalty method. In the context of internal dissipation in thermodynamics for incompressible flow with Boussinesq approximation, an energy conservation equation is appended that gives rise to a thermomechanically coupled system. The coupled fine-scale sub-problem is locally resolved to yield the closure model. The fine-scale turbulence features are accounted for by the VMS strategy wherein the hierarchical application of VMS results in further enhancement of the mass conservation. The new method for coupled systems is implemented using hexahedral and tetrahedral elements, and the code is parallelized for the distributed memory system. A range of problems is presented to show the mathematical and computational features of the method.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2021-12-01","The student, Lixing Zhu, accepted the attached license on 2019-12-02 at 15:46.","The student, Lixing Zhu, submitted this Dissertation for approval on 2019-12-02 at 17:53.","This Dissertation was approved for publication on 2019-12-04 at 08:50.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14647 on 2020-02-28 at 17:37:08","Made available in DSpace on 2020-03-02T22:38:49Z (GMT). No. of bitstreams: 3 ZHU-DISSERTATION-2019.pdf: 11297928 bytes, checksum: a291b57e719c378038dff8817adeab48 (MD5) LICENSE.txt: 4207 bytes, checksum: c640d4c132604d9ad051b48c4b63224c (MD5) PROQUEST_LICENSE.txt: 4553 bytes, checksum: 6e7f4ff11c6a43667054218368f258fa (MD5) Previous issue date: 2019-12-04","Embargo set by: Seth Robbins for item 114014 Lift date: 2022-03-02T22:39:04Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Open Restriction set for Item 114014 on 2021-01-29T17:08:06Z with date null by madinag@illinois.edu.","Open Restriction set for Item 114014 on 2021-01-29T17:08:11Z with date null by madinag@illinois.edu.","Open"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/106470"],"dc:language":["en"],"dc:rights":["Copyright 2019 Lixing Zhu"],"dc:subject":["Turbulent modelling","Variational Multiscale method","Arbitrary Lagrangian-Eulerian","Level-set method","Stratification","Free surfaces","Interface stabilization"],"dc:title":["Variational multiscale method for coupled systems: free-surface flows and stratified turbulence"],"dc:type":["text"],"thesis:degree_discipline":["Civil Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:47Z"}