{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/37228"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/37228","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Generalized spatial discretization techniques for space-marching algorithms","abstract":"Two unique spatial discretizations employing generalized indexing strategies suitable for use with space-marching algorithms are presented for the numerical solution of the equations of fluid dynamics. Both discretizations attempt to improve geometric flexibility as compared to structured indexing strategies and have been formulated while considering the current and future availability of unstructured grid generation techniques. The first discretization employs a generalized indexing strategy utilizing triangular elements in the two dimensions normal to the streamwise direction, while maintaining structure within the streamwise direction. The second discretization subdivides the domain into a collection of computational blocks. Each block has inflow and outflow boundaries suitable for space marching. A completely generalized indexing strategy utilizing tetrahedra is used within each computational block. The solution to the flow in each block is found independently in a fashion similar to the cross-flow planes of a structured discretization. Numerical algorithms have been developed for the solution of the governing equations on each of the two proposed discretizations. These spatial discretizations are obtained by applying a characteristic-based, upwind, finite volume scheme for the solution of the Euler equations. First-order and higher spatial accuracy is achieved with these implementations. A time dependent, space-marching algorithm is employed, with explicit time integration for convergence of individual computational blocks. Grid generation techniques suitable for the proposed discretizations are discussed. Applications of these discretization techniques include the high speed flow about a 5° cone, an analytic forebody, and a model SR71 aircraft.","abstract_html":"Two unique spatial discretizations employing generalized indexing strategies suitable for use with space-marching algorithms are presented for the numerical solution of the equations of fluid dynamics. Both discretizations attempt to improve geometric flexibility as compared to structured indexing strategies and have been formulated while considering the current and future availability of unstructured grid generation techniques. The first discretization employs a generalized indexing strategy utilizing triangular elements in the two dimensions normal to the streamwise direction, while maintaining structure within the streamwise direction. The second discretization subdivides the domain into a collection of computational blocks. Each block has inflow and outflow boundaries suitable for space marching. A completely generalized indexing strategy utilizing tetrahedra is used within each computational block. The solution to the flow in each block is found independently in a fashion similar to the cross-flow planes of a structured discretization. Numerical algorithms have been developed for the solution of the governing equations on each of the two proposed discretizations. These spatial discretizations are obtained by applying a characteristic-based, upwind, finite volume scheme for the solution of the Euler equations. First-order and higher spatial accuracy is achieved with these implementations. A time dependent, space-marching algorithm is employed, with explicit time integration for convergence of individual computational blocks. Grid generation techniques suitable for the proposed discretizations are discussed. Applications of these discretization techniques include the high speed flow about a 5° cone, an analytic forebody, and a model SR71 aircraft.","abstract_has_math":false,"creators":["McGrory, William Dandridge"],"institution":"Virginia Tech","degree_name":"Ph. D.","degree_level":"doctoral","degree_discipline":"Aerospace Engineering","degree_department":"Aerospace Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Walters, Robert W."],"committee_members":["Grossman, Bernard","Schetz, Joseph A.","Mason, William","Neu, Wayne"],"year":1991,"date_issued":"1991","date_published":"1991","updated_at":"2026-07-22T22:18:44Z","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-02012006-141710"],"render_values":[{"text":"etd-02012006-141710","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/37228","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Walters, Robert W."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Grossman, Bernard","Schetz, Joseph A.","Mason, William","Neu, Wayne"]},{"key":"dc:contributor.department","label":"Department","values":["Aerospace Engineering"]},{"key":"dc:creator","label":"Author","values":["McGrory, William Dandridge"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:08:57Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:08:57Z","2006-02-01"]},{"key":"dc:date.issued","label":"Date","values":["1991"]},{"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":["Aerospace 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-02012006-141710"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/37228"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Two unique spatial discretizations employing generalized indexing strategies suitable for use with space-marching algorithms are presented for the numerical solution of the equations of fluid dynamics. Both discretizations attempt to improve geometric flexibility as compared to structured indexing strategies and have been formulated while considering the current and future availability of unstructured grid generation techniques. The first discretization employs a generalized indexing strategy utilizing triangular elements in the two dimensions normal to the streamwise direction, while maintaining structure within the streamwise direction. The second discretization subdivides the domain into a collection of computational blocks. Each block has inflow and outflow boundaries suitable for space marching. A completely generalized indexing strategy utilizing tetrahedra is used within each computational block. The solution to the flow in each block is found independently in a fashion similar to the cross-flow planes of a structured discretization. Numerical algorithms have been developed for the solution of the governing equations on each of the two proposed discretizations. These spatial discretizations are obtained by applying a characteristic-based, upwind, finite volume scheme for the solution of the Euler equations. First-order and higher spatial accuracy is achieved with these implementations. A time dependent, space-marching algorithm is employed, with explicit time integration for convergence of individual computational blocks. Grid generation techniques suitable for the proposed discretizations are discussed. Applications of these discretization techniques include the high speed flow about a 5° cone, an analytic forebody, and a model SR71 aircraft."]},{"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":["Generalized spatial discretization techniques for space-marching algorithms"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Walters, Robert W."],"dc:contributor.committeemember":["Grossman, Bernard","Schetz, Joseph A.","Mason, William","Neu, Wayne"],"dc:contributor.department":["Aerospace Engineering"],"dc:creator":["McGrory, William Dandridge"],"dc:date.accessioned":["2014-03-14T21:08:57Z"],"dc:date.available":["2014-03-14T21:08:57Z","2006-02-01"],"dc:date.issued":["1991"],"dc:description.abstract":["Two unique spatial discretizations employing generalized indexing strategies suitable for use with space-marching algorithms are presented for the numerical solution of the equations of fluid dynamics. Both discretizations attempt to improve geometric flexibility as compared to structured indexing strategies and have been formulated while considering the current and future availability of unstructured grid generation techniques. The first discretization employs a generalized indexing strategy utilizing triangular elements in the two dimensions normal to the streamwise direction, while maintaining structure within the streamwise direction. The second discretization subdivides the domain into a collection of computational blocks. Each block has inflow and outflow boundaries suitable for space marching. A completely generalized indexing strategy utilizing tetrahedra is used within each computational block. The solution to the flow in each block is found independently in a fashion similar to the cross-flow planes of a structured discretization. Numerical algorithms have been developed for the solution of the governing equations on each of the two proposed discretizations. These spatial discretizations are obtained by applying a characteristic-based, upwind, finite volume scheme for the solution of the Euler equations. First-order and higher spatial accuracy is achieved with these implementations. A time dependent, space-marching algorithm is employed, with explicit time integration for convergence of individual computational blocks. Grid generation techniques suitable for the proposed discretizations are discussed. Applications of these discretization techniques include the high speed flow about a 5° cone, an analytic forebody, and a model SR71 aircraft."],"dc:description.degree":["Ph. D."],"dc:format.medium":["BTD"],"dc:format.mimetype":["application/pdf"],"dc:identifier.other":["etd-02012006-141710"],"dc:identifier.uri":["http://hdl.handle.net/10919/37228"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Generalized spatial discretization techniques for space-marching algorithms"],"dc:type":["Dissertation"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:18:44Z"}