An effort to improve the numerical accuracy of a three dimensional unstructured grid finite volume scheme is pursued in the present work. Unstructured grid methods have been widely used in computational fluid dynamics for the convenience of modeling complex geometries in realistic applications. In the present work, improvements towards high order unstructured grid schemes are proposed using high order flux formula for spatial discretizations. The Riemann variables on the left and right sides of the interface are reconstructed using quadratic and quartic polynomials composed of both flow variables and their gradients. The high order flux is then calculated using the concept of MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) approach. In order to maintain the accuracy for the finite volume scheme, an innovative method based on Radial Basis Function interpolation is introduced as a substitution to Gaussian quadrature to achieve the higher order surface integration on mixed element unstructured grids.
The proposed high order improvements for unstructured grid schemes have been tested for a wide range of flows from very low Mach number to supersonic speeds. The observed accuracy for the improved schemes is verified using a benchmark case about an inviscid vortex transporting in a free stream flow. In addition, the ability to capture the tip trailing vortex, which is a major challenge in computational fluid dynamics today, is extensively verified on two vortex dominated viscous flows, a fixed NACA0015 wing at a subsonic Mach number and a rotating NACA0012 hovering rotor at a transonic tip speed. The numerical validations are also performed on two realistic industrial applications including a marine propeller P5168 and a Bell Helicopter aircraft 427 main rotor. Computational results indicate that the methods proposed in the present work can significantly improve numerical accuracy in predicting the strong vortical flows in smooth regions, while maintaining the stability of the schemes in discontinuous regions such as shockwaves.
","abstract_html":"<p>An effort to improve the numerical accuracy of a three dimensional unstructured grid finite volume scheme is pursued in the present work. Unstructured grid methods have been widely used in computational fluid dynamics for the convenience of modeling complex geometries in realistic applications. In the present work, improvements towards high order unstructured grid schemes are proposed using high order flux formula for spatial discretizations. The Riemann variables on the left and right sides of the interface are reconstructed using quadratic and quartic polynomials composed of both flow variables and their gradients. The high order flux is then calculated using the concept of MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) approach. In order to maintain the accuracy for the finite volume scheme, an innovative method based on Radial Basis Function interpolation is introduced as a substitution to Gaussian quadrature to achieve the higher order surface integration on mixed element unstructured grids.</p><p>The proposed high order improvements for unstructured grid schemes have been tested for a wide range of flows from very low Mach number to supersonic speeds. The observed accuracy for the improved schemes is verified using a benchmark case about an inviscid vortex transporting in a free stream flow. In addition, the ability to capture the tip trailing vortex, which is a major challenge in computational fluid dynamics today, is extensively verified on two vortex dominated viscous flows, a fixed NACA0015 wing at a subsonic Mach number and a rotating NACA0012 hovering rotor at a transonic tip speed. The numerical validations are also performed on two realistic industrial applications including a marine propeller P5168 and a Bell Helicopter aircraft 427 main rotor. Computational results indicate that the methods proposed in the present work can significantly improve numerical accuracy in predicting the strong vortical flows in smooth regions, while maintaining the stability of the schemes in discontinuous regions such as shockwaves.</p>","abstract_has_math":false,"creators":["Zhao, Qiuying"],"institution":"University of Toledo","degree_name":"Doctor of Philosophy in Engineering","degree_level":"doctoral","degree_discipline":"College of Engineering","degree_department":null,"school":null,"contributors":["Sheng, Chunhua","Ng, Terry"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012","date_published":"2012","updated_at":"2026-07-24T03:36:23Z","subjects":["Aerospace Engineering","Engineering","Fluid Dynamics","Mechanical Engineering","CFD","Higher Order","Unstructured Grid","NS Equations"],"languages":["English"],"rights":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://rave.ohiolink.edu/etdc/view?acc_num=toledo1353107603","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Sheng, Chunhua","Ng, Terry"]},{"key":"dc:creator","label":"Author","values":["Zhao, Qiuying"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012"]},{"key":"dc:publisher","label":"Institution","values":["University of Toledo / OhioLINK"]},{"key":"dc:type","label":"Dc Type","values":["Electronic Thesis or Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["College of Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy in Engineering"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Toledo"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Aerospace Engineering","Engineering","Fluid Dynamics","Mechanical Engineering","CFD","Higher Order","Unstructured Grid","NS Equations"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://rave.ohiolink.edu/etdc/view?acc_num=toledo1353107603"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["An effort to improve the numerical accuracy of a three dimensional unstructured grid finite volume scheme is pursued in the present work. Unstructured grid methods have been widely used in computational fluid dynamics for the convenience of modeling complex geometries in realistic applications. In the present work, improvements towards high order unstructured grid schemes are proposed using high order flux formula for spatial discretizations. The Riemann variables on the left and right sides of the interface are reconstructed using quadratic and quartic polynomials composed of both flow variables and their gradients. The high order flux is then calculated using the concept of MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) approach. In order to maintain the accuracy for the finite volume scheme, an innovative method based on Radial Basis Function interpolation is introduced as a substitution to Gaussian quadrature to achieve the higher order surface integration on mixed element unstructured grids.
The proposed high order improvements for unstructured grid schemes have been tested for a wide range of flows from very low Mach number to supersonic speeds. The observed accuracy for the improved schemes is verified using a benchmark case about an inviscid vortex transporting in a free stream flow. In addition, the ability to capture the tip trailing vortex, which is a major challenge in computational fluid dynamics today, is extensively verified on two vortex dominated viscous flows, a fixed NACA0015 wing at a subsonic Mach number and a rotating NACA0012 hovering rotor at a transonic tip speed. The numerical validations are also performed on two realistic industrial applications including a marine propeller P5168 and a Bell Helicopter aircraft 427 main rotor. Computational results indicate that the methods proposed in the present work can significantly improve numerical accuracy in predicting the strong vortical flows in smooth regions, while maintaining the stability of the schemes in discontinuous regions such as shockwaves.
"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf","p.190","6.18 MB"]},{"key":"dc:title","label":"Title","values":["Towards Improvement of Numerical Accuracy for Unstructured Grid Flow Solver"]}]}],"canonical_facts":{"dc:contributor":["Sheng, Chunhua","Ng, Terry"],"dc:creator":["Zhao, Qiuying"],"dc:date":["2012"],"dc:description":["An effort to improve the numerical accuracy of a three dimensional unstructured grid finite volume scheme is pursued in the present work. Unstructured grid methods have been widely used in computational fluid dynamics for the convenience of modeling complex geometries in realistic applications. In the present work, improvements towards high order unstructured grid schemes are proposed using high order flux formula for spatial discretizations. The Riemann variables on the left and right sides of the interface are reconstructed using quadratic and quartic polynomials composed of both flow variables and their gradients. The high order flux is then calculated using the concept of MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) approach. In order to maintain the accuracy for the finite volume scheme, an innovative method based on Radial Basis Function interpolation is introduced as a substitution to Gaussian quadrature to achieve the higher order surface integration on mixed element unstructured grids.
The proposed high order improvements for unstructured grid schemes have been tested for a wide range of flows from very low Mach number to supersonic speeds. The observed accuracy for the improved schemes is verified using a benchmark case about an inviscid vortex transporting in a free stream flow. In addition, the ability to capture the tip trailing vortex, which is a major challenge in computational fluid dynamics today, is extensively verified on two vortex dominated viscous flows, a fixed NACA0015 wing at a subsonic Mach number and a rotating NACA0012 hovering rotor at a transonic tip speed. The numerical validations are also performed on two realistic industrial applications including a marine propeller P5168 and a Bell Helicopter aircraft 427 main rotor. Computational results indicate that the methods proposed in the present work can significantly improve numerical accuracy in predicting the strong vortical flows in smooth regions, while maintaining the stability of the schemes in discontinuous regions such as shockwaves.
"],"dc:format":["application/pdf","p.190","6.18 MB"],"dc:identifier":["http://rave.ohiolink.edu/etdc/view?acc_num=toledo1353107603"],"dc:language":["English"],"dc:publisher":["University of Toledo / OhioLINK"],"dc:rights":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws."],"dc:subject":["Aerospace Engineering","Engineering","Fluid Dynamics","Mechanical Engineering","CFD","Higher Order","Unstructured Grid","NS Equations"],"dc:title":["Towards Improvement of Numerical Accuracy for Unstructured Grid Flow Solver"],"dc:type":["Electronic Thesis or Dissertation"],"thesis:degree_discipline":["College of Engineering"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Doctor of Philosophy in Engineering"],"thesis:institution_name":["University of Toledo"]},"updated_at":"2026-07-24T03:36:23Z"}