In this thesis, molecular Couette flow is clearly defined and the modeling and simulation of this kind of flow is systematically investigated. First, the integral equations for the velocity of gaseous Couette flow and related flows are derived from linearized Boltzmann BGK equation with Maxwell boundary condition and solved with high precision by using Chebyshev collocation and chunk-based collocation methods. The velocity profiles of gaseous Couette flows and related flows with a wide range of Knudsen number and the Maxwell boundary condition of various accommodation ratios are obtained. Moreover, the order of convergence of the numerical methods is also discussed and I obtain better precision. Second, to model the velocity profile, the analysis of Couette flows with pure diffusive boundary condition is given. My results show that the velocity profile is most appropriately approximated by a cubic polynomial. Meanwhile, the analysis also discloses the Knudsen number dependences of microscopic and macroscopic slip velocities and of the half channel mass flow rate. Finally, the modeling and simulation of molecular Couette flow in Navier-Stokes framework is carried out. To obtain density and velocity profiles including the Van der Waals effects near walls, high Knudsen number gaseous Couette flows are simulated by using molecular dynamics simulation (MD). Based on high precision solutions of the integral equations and MD results of velocity and density, macroscopic moments of molecular Couette flows are modeled by using effective radial distribution functions. Then, with these modeled velocity and density profiles, the effective viscosity in the stress tensor of Navier-Stokes equation is constructed. The velocity and density profiles are reproduced by two-relaxation time lattice Boltzmann method in Navier-Stokes framework by the effective viscosity model.
","abstract_html":"<p>In this thesis, molecular Couette flow is clearly defined and the modeling and simulation of this kind of flow is systematically investigated. First, the integral equations for the velocity of gaseous Couette flow and related flows are derived from linearized Boltzmann BGK equation with Maxwell boundary condition and solved with high precision by using Chebyshev collocation and chunk-based collocation methods. The velocity profiles of gaseous Couette flows and related flows with a wide range of Knudsen number and the Maxwell boundary condition of various accommodation ratios are obtained. Moreover, the order of convergence of the numerical methods is also discussed and I obtain better precision. Second, to model the velocity profile, the analysis of Couette flows with pure diffusive boundary condition is given. My results show that the velocity profile is most appropriately approximated by a cubic polynomial. Meanwhile, the analysis also discloses the Knudsen number dependences of microscopic and macroscopic slip velocities and of the half channel mass flow rate. Finally, the modeling and simulation of molecular Couette flow in Navier-Stokes framework is carried out. To obtain density and velocity profiles including the Van der Waals effects near walls, high Knudsen number gaseous Couette flows are simulated by using molecular dynamics simulation (MD). Based on high precision solutions of the integral equations and MD results of velocity and density, macroscopic moments of molecular Couette flows are modeled by using effective radial distribution functions. Then, with these modeled velocity and density profiles, the effective viscosity in the stress tensor of Navier-Stokes equation is constructed. The velocity and density profiles are reproduced by two-relaxation time lattice Boltzmann method in Navier-Stokes framework by the effective viscosity model.</p>","abstract_has_math":false,"creators":["Li, Wei"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Li-Shi Luo","Richard Noren","Fang Q. Hu","Yan Peng","Taehun Lee"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-01T08:00:00Z","date_published":"2015-01-01T08:00:00Z","updated_at":"2026-07-24T03:34:53Z","subjects":["Collocation Methods","Couette Flow","Integral Equation","Lattice Boltzmann method","Molecular dynamics","Applied Mathematics"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["9781339876757"],"render_values":[{"text":"9781339876757","href":null,"code":true}]}]},"links":{"outbound_url":"https://digitalcommons.odu.edu/mathstat_etds/40","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Li-Shi Luo","Richard Noren","Fang Q. Hu","Yan Peng","Taehun Lee"]},{"key":"dc:creator","label":"Author","values":["Li, Wei"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-06-06T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics & Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Collocation Methods","Couette Flow","Integral Equation","Lattice Boltzmann method","Molecular dynamics","Applied Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["9781339876757","https://digitalcommons.odu.edu/mathstat_etds/40"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, molecular Couette flow is clearly defined and the modeling and simulation of this kind of flow is systematically investigated. First, the integral equations for the velocity of gaseous Couette flow and related flows are derived from linearized Boltzmann BGK equation with Maxwell boundary condition and solved with high precision by using Chebyshev collocation and chunk-based collocation methods. The velocity profiles of gaseous Couette flows and related flows with a wide range of Knudsen number and the Maxwell boundary condition of various accommodation ratios are obtained. Moreover, the order of convergence of the numerical methods is also discussed and I obtain better precision. Second, to model the velocity profile, the analysis of Couette flows with pure diffusive boundary condition is given. My results show that the velocity profile is most appropriately approximated by a cubic polynomial. Meanwhile, the analysis also discloses the Knudsen number dependences of microscopic and macroscopic slip velocities and of the half channel mass flow rate. Finally, the modeling and simulation of molecular Couette flow in Navier-Stokes framework is carried out. To obtain density and velocity profiles including the Van der Waals effects near walls, high Knudsen number gaseous Couette flows are simulated by using molecular dynamics simulation (MD). Based on high precision solutions of the integral equations and MD results of velocity and density, macroscopic moments of molecular Couette flows are modeled by using effective radial distribution functions. Then, with these modeled velocity and density profiles, the effective viscosity in the stress tensor of Navier-Stokes equation is constructed. The velocity and density profiles are reproduced by two-relaxation time lattice Boltzmann method in Navier-Stokes framework by the effective viscosity model.
"]},{"key":"dc:title","label":"Title","values":["Modeling and Simulation of Molecular Couette Flows and Related Flows"]}]}],"canonical_facts":{"dc:contributor":["Li-Shi Luo","Richard Noren","Fang Q. Hu","Yan Peng","Taehun Lee"],"dc:creator":["Li, Wei"],"dc:date.available":["2019-06-06T07:00:00Z"],"dc:description.abstract":["In this thesis, molecular Couette flow is clearly defined and the modeling and simulation of this kind of flow is systematically investigated. First, the integral equations for the velocity of gaseous Couette flow and related flows are derived from linearized Boltzmann BGK equation with Maxwell boundary condition and solved with high precision by using Chebyshev collocation and chunk-based collocation methods. The velocity profiles of gaseous Couette flows and related flows with a wide range of Knudsen number and the Maxwell boundary condition of various accommodation ratios are obtained. Moreover, the order of convergence of the numerical methods is also discussed and I obtain better precision. Second, to model the velocity profile, the analysis of Couette flows with pure diffusive boundary condition is given. My results show that the velocity profile is most appropriately approximated by a cubic polynomial. Meanwhile, the analysis also discloses the Knudsen number dependences of microscopic and macroscopic slip velocities and of the half channel mass flow rate. Finally, the modeling and simulation of molecular Couette flow in Navier-Stokes framework is carried out. To obtain density and velocity profiles including the Van der Waals effects near walls, high Knudsen number gaseous Couette flows are simulated by using molecular dynamics simulation (MD). Based on high precision solutions of the integral equations and MD results of velocity and density, macroscopic moments of molecular Couette flows are modeled by using effective radial distribution functions. Then, with these modeled velocity and density profiles, the effective viscosity in the stress tensor of Navier-Stokes equation is constructed. The velocity and density profiles are reproduced by two-relaxation time lattice Boltzmann method in Navier-Stokes framework by the effective viscosity model.
"],"dc:identifier":["9781339876757","https://digitalcommons.odu.edu/mathstat_etds/40"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Collocation Methods","Couette Flow","Integral Equation","Lattice Boltzmann method","Molecular dynamics","Applied Mathematics"],"dc:title":["Modeling and Simulation of Molecular Couette Flows and Related Flows"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:34:53Z"}