{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/38816"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/38816","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Near-wall similarity in three-dimensional turbulent boundary layers","abstract":"This work investigates three main topics. The first of these is the development and comparison of time integration schemes on two-dimensional unstructured meshes. Both explicit and implicit solution algorithms for the two-dimensional Euler equations on unstructured grids are presented. Cell-centered and cell-vertex finite volume upwind schemes utilizing Roe’s approximate Riemann solver are developed. For the cell-vertex scheme, a four stage Runge-Kutta time integration with and without implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method, and two methods utilizing preconditioned sparse matrix solvers are investigated. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit LU decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver in order to decrease CPU time by reducing the fill of the Jacobian matrix. Comparisons are made for both first-order and higher-order accurate solutions using several different time integration algorithms. Higher-order accuracy is achieved by using multi-dimensional monotone linear reconstruction procedures. Results for flow over a transonic circular arc are compared for the various time integration methods. The second topic involves an interactive adaptive remeshing algorithm. The interactive adaptive remeshing algorithm utilizing a frontal grid generator is compared to a single grid calculation. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. Solutions for two-dimensional, inviscid flow over a transonic circular arc and a Mach 3.0 internal flow with an area change are examined. The final topic examined in this work is the capabilities developed for a structured three-dimensional code called GASP. The capabilities include: generalized chemistry and thermodynamic modeling, space marching, memory management through the use of binary C Input/Ouput, and algebraic and two-equation eddy viscosity turbulence modeling. Results are given for a Mach 1.7 three-dimensional analytic forebody, a Mach 1.38 axisymmetric nozzle with hydrogen-air combustion, a Mach 14.1 15° ramp, and Mach 0.3 viscous flow over a flat plate. The incorporation of these capabilities and the two-dimensional unstructured time integration schemes into a three-dimensional unstructured solver is also discussed.","abstract_html":"This work investigates three main topics. The first of these is the development and comparison of time integration schemes on two-dimensional unstructured meshes. Both explicit and implicit solution algorithms for the two-dimensional Euler equations on unstructured grids are presented. Cell-centered and cell-vertex finite volume upwind schemes utilizing Roe’s approximate Riemann solver are developed. For the cell-vertex scheme, a four stage Runge-Kutta time integration with and without implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method, and two methods utilizing preconditioned sparse matrix solvers are investigated. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit LU decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver in order to decrease CPU time by reducing the fill of the Jacobian matrix. Comparisons are made for both first-order and higher-order accurate solutions using several different time integration algorithms. Higher-order accuracy is achieved by using multi-dimensional monotone linear reconstruction procedures. Results for flow over a transonic circular arc are compared for the various time integration methods. The second topic involves an interactive adaptive remeshing algorithm. The interactive adaptive remeshing algorithm utilizing a frontal grid generator is compared to a single grid calculation. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. Solutions for two-dimensional, inviscid flow over a transonic circular arc and a Mach 3.0 internal flow with an area change are examined. The final topic examined in this work is the capabilities developed for a structured three-dimensional code called GASP. The capabilities include: generalized chemistry and thermodynamic modeling, space marching, memory management through the use of binary C Input/Ouput, and algebraic and two-equation eddy viscosity turbulence modeling. Results are given for a Mach 1.7 three-dimensional analytic forebody, a Mach 1.38 axisymmetric nozzle with hydrogen-air combustion, a Mach 14.1 15° ramp, and Mach 0.3 viscous flow over a flat plate. The incorporation of these capabilities and the two-dimensional unstructured time integration schemes into a three-dimensional unstructured solver is also discussed.","abstract_has_math":false,"creators":["Tennant, Mark Harris"],"institution":"Virginia Tech","degree_name":"Ph. D.","degree_level":"doctoral","degree_discipline":"Mechanical Engineering","degree_department":"Mechanical Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1977,"date_issued":"1977","date_published":"1977","updated_at":"2026-07-22T22:19:13Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-07152010-020350"],"render_values":[{"text":"etd-07152010-020350","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/38816","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Mechanical Engineering"]},{"key":"dc:creator","label":"Author","values":["Tennant, Mark Harris"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:16:12Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:16:12Z","2010-07-15"]},{"key":"dc:date.issued","label":"Date","values":["1977"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-07152010-020350"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/38816"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This work investigates three main topics. The first of these is the development and comparison of time integration schemes on two-dimensional unstructured meshes. Both explicit and implicit solution algorithms for the two-dimensional Euler equations on unstructured grids are presented. Cell-centered and cell-vertex finite volume upwind schemes utilizing Roe’s approximate Riemann solver are developed. For the cell-vertex scheme, a four stage Runge-Kutta time integration with and without implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method, and two methods utilizing preconditioned sparse matrix solvers are investigated. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit LU decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver in order to decrease CPU time by reducing the fill of the Jacobian matrix. Comparisons are made for both first-order and higher-order accurate solutions using several different time integration algorithms. Higher-order accuracy is achieved by using multi-dimensional monotone linear reconstruction procedures. Results for flow over a transonic circular arc are compared for the various time integration methods. The second topic involves an interactive adaptive remeshing algorithm. The interactive adaptive remeshing algorithm utilizing a frontal grid generator is compared to a single grid calculation. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. Solutions for two-dimensional, inviscid flow over a transonic circular arc and a Mach 3.0 internal flow with an area change are examined. The final topic examined in this work is the capabilities developed for a structured three-dimensional code called GASP. The capabilities include: generalized chemistry and thermodynamic modeling, space marching, memory management through the use of binary C Input/Ouput, and algebraic and two-equation eddy viscosity turbulence modeling. Results are given for a Mach 1.7 three-dimensional analytic forebody, a Mach 1.38 axisymmetric nozzle with hydrogen-air combustion, a Mach 14.1 15° ramp, and Mach 0.3 viscous flow over a flat plate. The incorporation of these capabilities and the two-dimensional unstructured time integration schemes into a three-dimensional unstructured solver is also discussed."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Near-wall similarity in three-dimensional turbulent boundary layers"]}]}],"canonical_facts":{"dc:contributor.department":["Mechanical Engineering"],"dc:creator":["Tennant, Mark Harris"],"dc:date.accessioned":["2014-03-14T21:16:12Z"],"dc:date.available":["2014-03-14T21:16:12Z","2010-07-15"],"dc:date.issued":["1977"],"dc:description.abstract":["This work investigates three main topics. The first of these is the development and comparison of time integration schemes on two-dimensional unstructured meshes. Both explicit and implicit solution algorithms for the two-dimensional Euler equations on unstructured grids are presented. Cell-centered and cell-vertex finite volume upwind schemes utilizing Roe’s approximate Riemann solver are developed. For the cell-vertex scheme, a four stage Runge-Kutta time integration with and without implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method, and two methods utilizing preconditioned sparse matrix solvers are investigated. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit LU decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver in order to decrease CPU time by reducing the fill of the Jacobian matrix. Comparisons are made for both first-order and higher-order accurate solutions using several different time integration algorithms. Higher-order accuracy is achieved by using multi-dimensional monotone linear reconstruction procedures. Results for flow over a transonic circular arc are compared for the various time integration methods. The second topic involves an interactive adaptive remeshing algorithm. The interactive adaptive remeshing algorithm utilizing a frontal grid generator is compared to a single grid calculation. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. Solutions for two-dimensional, inviscid flow over a transonic circular arc and a Mach 3.0 internal flow with an area change are examined. The final topic examined in this work is the capabilities developed for a structured three-dimensional code called GASP. The capabilities include: generalized chemistry and thermodynamic modeling, space marching, memory management through the use of binary C Input/Ouput, and algebraic and two-equation eddy viscosity turbulence modeling. Results are given for a Mach 1.7 three-dimensional analytic forebody, a Mach 1.38 axisymmetric nozzle with hydrogen-air combustion, a Mach 14.1 15° ramp, and Mach 0.3 viscous flow over a flat plate. The incorporation of these capabilities and the two-dimensional unstructured time integration schemes into a three-dimensional unstructured solver is also discussed."],"dc:description.degree":["Ph. D."],"dc:format.medium":["BTD"],"dc:format.mimetype":["application/pdf"],"dc:identifier.other":["etd-07152010-020350"],"dc:identifier.uri":["http://hdl.handle.net/10919/38816"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Near-wall similarity in three-dimensional turbulent boundary layers"],"dc:type":["Dissertation"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:13Z"}