{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/118593"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/118593","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Error Transport Equations for Unsteady Discontinuous Applications","abstract":"Computational Fluid Dynamics (CFD) has been pivotal in scientific computing, providing critical insights into complex fluid dynamics unattainable through traditional experimental methods. Despite its widespread use, the accuracy of CFD results remains contingent upon the underlying modeling and numerical errors. A key aspect of ensuring simulation reliability is the accurate quantification of discretization error (DE), which is the difference between the simulation solution and the exact solution in the physical world. This study addresses quantifying DE through Error Transport Equations (ETE), which are an additional set of equations capable of quantifying the local DE in a solution. Historically, Richardson extrapolation has been a mainstay for DE estimation due to its simplicity and effectiveness. However, the method's feasibility diminishes with increasing computational demands, particularly in large-scale and high-dimensional problems. The integration of ETE into existing CFD frameworks is facilitated by their compatibility with existing numerical codes, minimizing the need for extensive code modification. By incorporating techniques developed for managing discontinuities, the study broadens ETE applicability to a wider range of scientific computing applications, particularly those involving complex, unsteady flows. The culmination of this research is demonstrated on unsteady discontinuous problems, such as Sod's problem.","abstract_html":"Computational Fluid Dynamics (CFD) has been pivotal in scientific computing, providing critical insights into complex fluid dynamics unattainable through traditional experimental methods. Despite its widespread use, the accuracy of CFD results remains contingent upon the underlying modeling and numerical errors. A key aspect of ensuring simulation reliability is the accurate quantification of discretization error (DE), which is the difference between the simulation solution and the exact solution in the physical world. This study addresses quantifying DE through Error Transport Equations (ETE), which are an additional set of equations capable of quantifying the local DE in a solution. Historically, Richardson extrapolation has been a mainstay for DE estimation due to its simplicity and effectiveness. However, the method's feasibility diminishes with increasing computational demands, particularly in large-scale and high-dimensional problems. The integration of ETE into existing CFD frameworks is facilitated by their compatibility with existing numerical codes, minimizing the need for extensive code modification. By incorporating techniques developed for managing discontinuities, the study broadens ETE applicability to a wider range of scientific computing applications, particularly those involving complex, unsteady flows. The culmination of this research is demonstrated on unsteady discontinuous problems, such as Sod's problem.","abstract_has_math":false,"creators":["Ganotaki, Michael"],"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 John"],"committee_members":["Ferguson, Jim","Massa, Luca"],"year":2024,"date_issued":"2024-04-02","date_published":"2024-04-02","updated_at":"2026-07-22T22:20:34Z","subjects":["Error estimation","CFD","Discontinuities"],"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":["vt_gsexam:39771"],"render_values":[{"text":"vt_gsexam:39771","href":null,"code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10919/118593","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 John"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Ferguson, Jim","Massa, Luca"]},{"key":"dc:contributor.department","label":"Department","values":["Aerospace and Ocean Engineering"]},{"key":"dc:creator","label":"Author","values":["Ganotaki, Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-04-17T16:31:08Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-04-17T16:31:08Z"]},{"key":"dc:date.issued","label":"Date","values":["2024-04-02"]},{"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":["Error estimation","CFD","Discontinuities"]}]},{"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":["vt_gsexam:39771"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10919/118593"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Computational Fluid Dynamics (CFD) has been pivotal in scientific computing, providing critical insights into complex fluid dynamics unattainable through traditional experimental methods. Despite its widespread use, the accuracy of CFD results remains contingent upon the underlying modeling and numerical errors. A key aspect of ensuring simulation reliability is the accurate quantification of discretization error (DE), which is the difference between the simulation solution and the exact solution in the physical world. This study addresses quantifying DE through Error Transport Equations (ETE), which are an additional set of equations capable of quantifying the local DE in a solution. Historically, Richardson extrapolation has been a mainstay for DE estimation due to its simplicity and effectiveness. However, the method's feasibility diminishes with increasing computational demands, particularly in large-scale and high-dimensional problems. The integration of ETE into existing CFD frameworks is facilitated by their compatibility with existing numerical codes, minimizing the need for extensive code modification. By incorporating techniques developed for managing discontinuities, the study broadens ETE applicability to a wider range of scientific computing applications, particularly those involving complex, unsteady flows. The culmination of this research is demonstrated on unsteady discontinuous problems, such as Sod's problem."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["In the ever-evolving field of Computational Fluid Dynamics (CFD), the quest for accuracy is paramount. This thesis focuses on discretization error estimation within CFD simulations, specifically on the challenge of predicting fluid behavior in scenarios marked by sudden changes, such as shock waves. At the core of this work lies an error estimation tool known as Error Transport Equations (ETE) to improve the numerical accuracy of simulations involving unsteady flows and discontinuities. Traditionally, the accuracy of CFD simulations has been limited by discretization errors, generally the largest numerical error, which is the difference between the numerical solution and the exact solution. With ETE, this research identifies these errors to enhance the simulation's overall accuracy. The implications of ETE research are far-reaching. Improved error estimation and correction methods can lead to more reliable predictions in a wide range of applications, from aeronautical engineering, where the aerodynamics of aircraft is critical, to plasma science, with applications in fusion and deep space propulsion."]},{"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":["Error Transport Equations for Unsteady Discontinuous Applications"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Roy, Christopher John"],"dc:contributor.committeemember":["Ferguson, Jim","Massa, Luca"],"dc:contributor.department":["Aerospace and Ocean Engineering"],"dc:creator":["Ganotaki, Michael"],"dc:date.accessioned":["2024-04-17T16:31:08Z"],"dc:date.available":["2024-04-17T16:31:08Z"],"dc:date.issued":["2024-04-02"],"dc:description.abstract":["Computational Fluid Dynamics (CFD) has been pivotal in scientific computing, providing critical insights into complex fluid dynamics unattainable through traditional experimental methods. 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By incorporating techniques developed for managing discontinuities, the study broadens ETE applicability to a wider range of scientific computing applications, particularly those involving complex, unsteady flows. The culmination of this research is demonstrated on unsteady discontinuous problems, such as Sod's problem."],"dc:description.abstractgeneral":["In the ever-evolving field of Computational Fluid Dynamics (CFD), the quest for accuracy is paramount. This thesis focuses on discretization error estimation within CFD simulations, specifically on the challenge of predicting fluid behavior in scenarios marked by sudden changes, such as shock waves. At the core of this work lies an error estimation tool known as Error Transport Equations (ETE) to improve the numerical accuracy of simulations involving unsteady flows and discontinuities. Traditionally, the accuracy of CFD simulations has been limited by discretization errors, generally the largest numerical error, which is the difference between the numerical solution and the exact solution. With ETE, this research identifies these errors to enhance the simulation's overall accuracy. The implications of ETE research are far-reaching. Improved error estimation and correction methods can lead to more reliable predictions in a wide range of applications, from aeronautical engineering, where the aerodynamics of aircraft is critical, to plasma science, with applications in fusion and deep space propulsion."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:39771"],"dc:identifier.uri":["https://hdl.handle.net/10919/118593"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Error estimation","CFD","Discontinuities"],"dc:title":["Error Transport Equations for Unsteady Discontinuous Applications"],"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":"2026-07-22T22:20:34Z"}