{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/96400"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/96400","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Residual-Based Discretization Error Estimation for Unsteady Flows","abstract":"Computational fluid dynamics (CFD) is a tool that is widely used in most industries today. It is important to have rigorous techniques to estimate the error produced when using CFD. This thesis develops techniques to estimate discretization error for unsteady flows using the unsteady error transport equation (ETE) as well as defect correction. A framework to obtain exact truncation error and estimated truncation error is also presented. The technique and results for the steady-state cases are given and the algorithm used for the steady case is extended for the unsteady case. Numerical results are presented for the steady viscous Burgers' equation, unsteady viscous Burgers' equation, steady quasi-1D Euler equations, and unsteady 1D Euler equations when applied to a shock tube. Cases using either defect correction or ETE are shown to give higher orders of accuracy for the corrected discretization error estimates when compared to the discretization error of the primal solution.","abstract_html":"Computational fluid dynamics (CFD) is a tool that is widely used in most industries today. It is important to have rigorous techniques to estimate the error produced when using CFD. This thesis develops techniques to estimate discretization error for unsteady flows using the unsteady error transport equation (ETE) as well as defect correction. A framework to obtain exact truncation error and estimated truncation error is also presented. The technique and results for the steady-state cases are given and the algorithm used for the steady case is extended for the unsteady case. Numerical results are presented for the steady viscous Burgers' equation, unsteady viscous Burgers' equation, steady quasi-1D Euler equations, and unsteady 1D Euler equations when applied to a shock tube. Cases using either defect correction or ETE are shown to give higher orders of accuracy for the corrected discretization error estimates when compared to the discretization error of the primal solution.","abstract_has_math":false,"creators":["Gautham, Tejaswini"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Aerospace Engineering","degree_department":"Aerospace and Ocean Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Roy, Christopher J."],"committee_members":["Xiao, Heng","Borggaard, Jeffrey T."],"year":2020,"date_issued":"2020-01-10","date_published":"2020-01-10","updated_at":"2026-07-22T22:20:07Z","subjects":["Computational fluid dynamics","truncation error","discretization error"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:23665"],"render_values":[{"text":"vt_gsexam:23665","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/96400","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Roy, Christopher J."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Xiao, Heng","Borggaard, Jeffrey T."]},{"key":"dc:contributor.department","label":"Department","values":["Aerospace and Ocean Engineering"]},{"key":"dc:creator","label":"Author","values":["Gautham, Tejaswini"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-01-11T09:01:08Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-01-11T09:01:08Z"]},{"key":"dc:date.issued","label":"Date","values":["2020-01-10"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace 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":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Computational fluid dynamics","truncation error","discretization error"]}]},{"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":["vt_gsexam:23665"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/96400"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Computational fluid dynamics (CFD) is a tool that is widely used in most industries today. It is important to have rigorous techniques to estimate the error produced when using CFD. This thesis develops techniques to estimate discretization error for unsteady flows using the unsteady error transport equation (ETE) as well as defect correction. A framework to obtain exact truncation error and estimated truncation error is also presented. The technique and results for the steady-state cases are given and the algorithm used for the steady case is extended for the unsteady case. Numerical results are presented for the steady viscous Burgers' equation, unsteady viscous Burgers' equation, steady quasi-1D Euler equations, and unsteady 1D Euler equations when applied to a shock tube. Cases using either defect correction or ETE are shown to give higher orders of accuracy for the corrected discretization error estimates when compared to the discretization error of the primal solution."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["Computational fluid dynamics (CFD) is a tool that is widely used in most industries today. It is used to understand complex flows that are difficult to replicate using experimental techniques or by theoretical methods. It is important to have rigorous techniques to estimate the error produced when using CFD even when the exact solution is not available for comparison. This paper develops techniques to estimate discretization error for unsteady flows. Discretization error has one of the largest error magnitudes in CFD solutions. The exact physics dictates the use of continuous equations but to apply CFD techniques, the continuous equations have to be converted to discrete equations. Truncation error is, the error obtained when converting the continuous equations to discrete equations. This truncation error is in turn, the local source term for discretization error. To reduce the discretization error in the discrete equations, the exact or estimated truncation error is either added as a source term to the discrete equations or is used along with the error transport equation to get a better estimate of the solutions. A framework to obtain exact truncation error and estimated truncation error is also presented. The framework is first applied to the steady equations and is verified with results from previous studies and is then extended to the unsteady flows."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Residual-Based Discretization Error Estimation for Unsteady Flows"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Roy, Christopher J."],"dc:contributor.committeemember":["Xiao, Heng","Borggaard, Jeffrey T."],"dc:contributor.department":["Aerospace and Ocean Engineering"],"dc:creator":["Gautham, Tejaswini"],"dc:date.accessioned":["2020-01-11T09:01:08Z"],"dc:date.available":["2020-01-11T09:01:08Z"],"dc:date.issued":["2020-01-10"],"dc:description.abstract":["Computational fluid dynamics (CFD) is a tool that is widely used in most industries today. It is important to have rigorous techniques to estimate the error produced when using CFD. This thesis develops techniques to estimate discretization error for unsteady flows using the unsteady error transport equation (ETE) as well as defect correction. A framework to obtain exact truncation error and estimated truncation error is also presented. The technique and results for the steady-state cases are given and the algorithm used for the steady case is extended for the unsteady case. Numerical results are presented for the steady viscous Burgers' equation, unsteady viscous Burgers' equation, steady quasi-1D Euler equations, and unsteady 1D Euler equations when applied to a shock tube. 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Truncation error is, the error obtained when converting the continuous equations to discrete equations. This truncation error is in turn, the local source term for discretization error. To reduce the discretization error in the discrete equations, the exact or estimated truncation error is either added as a source term to the discrete equations or is used along with the error transport equation to get a better estimate of the solutions. A framework to obtain exact truncation error and estimated truncation error is also presented. The framework is first applied to the steady equations and is verified with results from previous studies and is then extended to the unsteady flows."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:23665"],"dc:identifier.uri":["http://hdl.handle.net/10919/96400"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Computational fluid dynamics","truncation error","discretization error"],"dc:title":["Residual-Based Discretization Error Estimation for Unsteady Flows"],"dc:type":["Thesis"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:07Z"}