{"id":{"repo_id":"toronto-retro","oai_identifier":"oai:utoronto.scholaris.ca:1807/67314"},"canonical_url":"https://search.dev.ndltd.org/etd/toronto-retro/oai:utoronto.scholaris.ca:1807/67314","repository":{"repo_id":"toronto-retro","name":"University of Toronto","base_url":"https://utoronto.scholaris.ca/server/oai/request"},"display":{"title":"Finite Element Simulation of Interfacial Flows on Unstructured Meshes using a Second-order Accurate VOF Method","abstract":"This thesis consists of two major parts. In the first part a two-dimensional numerical model of interfacial flow phenomena has been developed, consisting of a finite element discretization of the time-dependent Navier-Stokes equations for immiscible, Newtonian, laminar, isothermal incompressible flows, with a volume-of-fluid (VOF) technique for interface capturing. A new formulation of the pressure Poisson equation that requires the discretization of a second-order derivative is used for the flow field on a fixed Eulerian grid. This approach enables us, in particular, to implement equal-order interpolation for the velocity and pressure. Streamline upwind Petrov-Galerkin (SUPG) stabilization is used for convection-dominated flows. Fluid interfaces are reconstructed and advected using a second-order accurate VOF method. An accurate least-squares circle-fit technique has been developed for curvature calculation on triangular meshes, and then used to implement surface tension forces on a single layer of interface elements. A dynamic contact angle model is implemented based on the Kistler correlation, that serves as a means to evaluate the dynamic contact angle as a function of grid-spacing and the contact-line velocity. Two-fluid flows with density ratios ranging from 10 to 106 are simulated, and the performance of the model is evaluated via the static-drop test case and several examples of bubble dynamics. Finally, the model is applied to the coalescence of two bubbles, the merging of a bubble into a free surface, and the impact of a glycerin droplet onto horizontal wax and glass surfaces, and yields good agreement with experimental measurements and other numerical results. In the second part, a second-order accurate three-dimensional VOF method for unstructured tetrahedral meshes has been developed. The method approximates interface geometries as piecewise planar, and advects volume via a forward trajectory remapping method. Two different methods are used to calculate the interface normal: a differential least-squares (DLS) method that is first-order accurate, and a geometric least-squares (GLS) method that is second-order accurate. Second-order accuracy of the VOF algorithm is demonstrated for simple translations and rotations as well as vigorous threedimensional vortex deformation.","abstract_html":"This thesis consists of two major parts. In the first part a two-dimensional numerical model of interfacial flow phenomena has been developed, consisting of a finite element discretization of the time-dependent Navier-Stokes equations for immiscible, Newtonian, laminar, isothermal incompressible flows, with a volume-of-fluid (VOF) technique for interface capturing. A new formulation of the pressure Poisson equation that requires the discretization of a second-order derivative is used for the flow field on a fixed Eulerian grid. This approach enables us, in particular, to implement equal-order interpolation for the velocity and pressure. Streamline upwind Petrov-Galerkin (SUPG) stabilization is used for convection-dominated flows. Fluid interfaces are reconstructed and advected using a second-order accurate VOF method. An accurate least-squares circle-fit technique has been developed for curvature calculation on triangular meshes, and then used to implement surface tension forces on a single layer of interface elements. A dynamic contact angle model is implemented based on the Kistler correlation, that serves as a means to evaluate the dynamic contact angle as a function of grid-spacing and the contact-line velocity. Two-fluid flows with density ratios ranging from 10 to 106 are simulated, and the performance of the model is evaluated via the static-drop test case and several examples of bubble dynamics. Finally, the model is applied to the coalescence of two bubbles, the merging of a bubble into a free surface, and the impact of a glycerin droplet onto horizontal wax and glass surfaces, and yields good agreement with experimental measurements and other numerical results. In the second part, a second-order accurate three-dimensional VOF method for unstructured tetrahedral meshes has been developed. The method approximates interface geometries as piecewise planar, and advects volume via a forward trajectory remapping method. Two different methods are used to calculate the interface normal: a differential least-squares (DLS) method that is first-order accurate, and a geometric least-squares (GLS) method that is second-order accurate. Second-order accuracy of the VOF algorithm is demonstrated for simple translations and rotations as well as vigorous threedimensional vortex deformation.","abstract_has_math":false,"creators":["Sultana, Zakia"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Mechanical and Industrial Engineering","school":null,"contributors":[],"advisors":["Mostaghimi, Javad","Paraschivoiu, Marius"],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-11","date_published":"2014-11","updated_at":"2026-07-27T21:27:52Z","subjects":["FEM","Interfacial flow","VOF"],"languages":["en_ca"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1807/67314","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Mostaghimi, Javad","Paraschivoiu, Marius"]},{"key":"dc:contributor.department","label":"Department","values":["Mechanical and Industrial Engineering"]},{"key":"dc:creator","label":"Author","values":["Sultana, Zakia"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-11"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-12-28T16:35:40Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["WITHHELD_TWO_YEAR","2014-12-28T16:35:40Z"]},{"key":"dc:date.issued","label":"Date","values":["2014-11"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["FEM","Interfacial flow","VOF"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_ca"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1807/67314"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis consists of two major parts. In the first part a two-dimensional numerical model of interfacial flow phenomena has been developed, consisting of a finite element discretization of the time-dependent Navier-Stokes equations for immiscible, Newtonian, laminar, isothermal incompressible flows, with a volume-of-fluid (VOF) technique for interface capturing. A new formulation of the pressure Poisson equation that requires the discretization of a second-order derivative is used for the flow field on a fixed Eulerian grid. This approach enables us, in particular, to implement equal-order interpolation for the velocity and pressure. Streamline upwind Petrov-Galerkin (SUPG) stabilization is used for convection-dominated flows. Fluid interfaces are reconstructed and advected using a second-order accurate VOF method. An accurate least-squares circle-fit technique has been developed for curvature calculation on triangular meshes, and then used to implement surface tension forces on a single layer of interface elements. A dynamic contact angle model is implemented based on the Kistler correlation, that serves as a means to evaluate the dynamic contact angle as a function of grid-spacing and the contact-line velocity. Two-fluid flows with density ratios ranging from 10 to 106 are simulated, and the performance of the model is evaluated via the static-drop test case and several examples of bubble dynamics. Finally, the model is applied to the coalescence of two bubbles, the merging of a bubble into a free surface, and the impact of a glycerin droplet onto horizontal wax and glass surfaces, and yields good agreement with experimental measurements and other numerical results. In the second part, a second-order accurate three-dimensional VOF method for unstructured tetrahedral meshes has been developed. The method approximates interface geometries as piecewise planar, and advects volume via a forward trajectory remapping method. Two different methods are used to calculate the interface normal: a differential least-squares (DLS) method that is first-order accurate, and a geometric least-squares (GLS) method that is second-order accurate. Second-order accuracy of the VOF algorithm is demonstrated for simple translations and rotations as well as vigorous threedimensional vortex deformation."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["PhD"]},{"key":"dc:title","label":"Title","values":["Finite Element Simulation of Interfacial Flows on Unstructured Meshes using a Second-order Accurate VOF Method"]}]}],"canonical_facts":{"dc:contributor.advisor":["Mostaghimi, Javad","Paraschivoiu, Marius"],"dc:contributor.department":["Mechanical and Industrial Engineering"],"dc:creator":["Sultana, Zakia"],"dc:date":["2014-11"],"dc:date.accessioned":["2014-12-28T16:35:40Z"],"dc:date.available":["WITHHELD_TWO_YEAR","2014-12-28T16:35:40Z"],"dc:date.issued":["2014-11"],"dc:description.abstract":["This thesis consists of two major parts. In the first part a two-dimensional numerical model of interfacial flow phenomena has been developed, consisting of a finite element discretization of the time-dependent Navier-Stokes equations for immiscible, Newtonian, laminar, isothermal incompressible flows, with a volume-of-fluid (VOF) technique for interface capturing. A new formulation of the pressure Poisson equation that requires the discretization of a second-order derivative is used for the flow field on a fixed Eulerian grid. This approach enables us, in particular, to implement equal-order interpolation for the velocity and pressure. Streamline upwind Petrov-Galerkin (SUPG) stabilization is used for convection-dominated flows. Fluid interfaces are reconstructed and advected using a second-order accurate VOF method. An accurate least-squares circle-fit technique has been developed for curvature calculation on triangular meshes, and then used to implement surface tension forces on a single layer of interface elements. A dynamic contact angle model is implemented based on the Kistler correlation, that serves as a means to evaluate the dynamic contact angle as a function of grid-spacing and the contact-line velocity. Two-fluid flows with density ratios ranging from 10 to 106 are simulated, and the performance of the model is evaluated via the static-drop test case and several examples of bubble dynamics. Finally, the model is applied to the coalescence of two bubbles, the merging of a bubble into a free surface, and the impact of a glycerin droplet onto horizontal wax and glass surfaces, and yields good agreement with experimental measurements and other numerical results. In the second part, a second-order accurate three-dimensional VOF method for unstructured tetrahedral meshes has been developed. The method approximates interface geometries as piecewise planar, and advects volume via a forward trajectory remapping method. Two different methods are used to calculate the interface normal: a differential least-squares (DLS) method that is first-order accurate, and a geometric least-squares (GLS) method that is second-order accurate. Second-order accuracy of the VOF algorithm is demonstrated for simple translations and rotations as well as vigorous threedimensional vortex deformation."],"dc:description.degree":["PhD"],"dc:identifier.uri":["http://hdl.handle.net/1807/67314"],"dc:language.iso":["en_ca"],"dc:subject":["FEM","Interfacial flow","VOF"],"dc:title":["Finite Element Simulation of Interfacial Flows on Unstructured Meshes using a Second-order Accurate VOF Method"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T21:27:52Z"}