{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/43052"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/43052","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Viscous solutions for the Navier Stokes equations using an upwind finite volume technique","abstract":"The process of enhancing an upwind finite volume, two-dimensional, thin layer Navier Stokes solver to achieve complete Navier Stokes solutions is described. The shear stress and heat flux contributions are identified and transformed to a generalized coordinate system. The metrics which result from the transformation have a geometrical interpretation in the finite volume formulation and are presented as supporting material. The additional terms which are neglected in the thin-layer approximations, are evaluated and discretized consistently with the finite volume method. Implicit linearizations are applied to the second derivatives tangent to the body surface; however, the cross derivatives are not linearized and are treated conservatively. Validation of the Navier Stokes solver is acquired by comparison to existing computational solutions for a double throat nozzle. Additional viscous solutions for the thin layer and the complete forms of the NS equations are provided for a flat plate shock boundary layer interaction.","abstract_html":"The process of enhancing an upwind finite volume, two-dimensional, thin layer Navier Stokes solver to achieve complete Navier Stokes solutions is described. The shear stress and heat flux contributions are identified and transformed to a generalized coordinate system. The metrics which result from the transformation have a geometrical interpretation in the finite volume formulation and are presented as supporting material. The additional terms which are neglected in the thin-layer approximations, are evaluated and discretized consistently with the finite volume method. Implicit linearizations are applied to the second derivatives tangent to the body surface; however, the cross derivatives are not linearized and are treated conservatively. Validation of the Navier Stokes solver is acquired by comparison to existing computational solutions for a double throat nozzle. Additional viscous solutions for the thin layer and the complete forms of the NS equations are provided for a flat plate shock boundary layer interaction.","abstract_has_math":false,"creators":["Mitchell, Curtis R."],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mechanical Engineering","degree_department":"Mechanical Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Ng, Wing Fai"],"committee_members":["Moses, Hal L.","Brown, Eugene F."],"year":1988,"date_issued":"1988-05-05","date_published":"1988-05-05","updated_at":"2026-07-22T22:19:19Z","subjects":[],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-06102012-040247"],"render_values":[{"text":"etd-06102012-040247","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/43052","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Ng, Wing Fai"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Moses, Hal L.","Brown, Eugene F."]},{"key":"dc:contributor.department","label":"Department","values":["Mechanical Engineering"]},{"key":"dc:creator","label":"Author","values":["Mitchell, Curtis R."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:37:40Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:37:40Z","2012-06-10"]},{"key":"dc:date.issued","label":"Date","values":["1988-05-05"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"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":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"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: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-06102012-040247"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/43052"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The process of enhancing an upwind finite volume, two-dimensional, thin layer Navier Stokes solver to achieve complete Navier Stokes solutions is described. 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