{"id":{"repo_id":"maryland","oai_identifier":"oai:drum.lib.umd.edu:1903/29312"},"canonical_url":"https://search.dev.ndltd.org/etd/maryland/oai:drum.lib.umd.edu:1903/29312","repository":{"repo_id":"maryland","name":"University of Maryland","base_url":"https://api.drum.lib.umd.edu/server/oai/request"},"display":{"title":"High Resolution Time-Limiter Schemes for Conservation Laws","abstract":"This study investigates the high resolution time-limiter schemes for conservation laws. These schemes are proposed (K.Duraisamy, J.D.Baeder, J-G Liu, 2003) to enhance the stability of high order implicit time marching when the time step is beyond the original TVD limit. The improved stability is realized by taking local convex combination of a higher order oscillatory method (accurate mode) with a first order unconditionally TVD method (stable mode). The application of time-limiters, which detects the local smoothness, enables the self-adjusting switch between different modes. One of the main aspects of this work is employing time-limiters to improve the stability of the strongly S-stable DIRK3 scheme, which is shown to be non-SSP and thus may generate strong oscillations in non-smooth problems. The new Limited-DIRK3 scheme (L-DIRK3) is proposed. For convenience of applications to systems of equations, we also propose a new and convenient construction of time-limiter, which allows an arbitrary choice of reference quantity with minimal computation cost. Another innovation of our work is the extension of time-limiter schemes to multi-dimensional problems and convection-diffusion problems. The numerical results for one- and two-dimensional problems confirm that the L-DIRK3 scheme generate high resolution and less oscillatory solutions under large time step. Particularly, the L-DIRK3 scheme shows a clear improvement against the original DIRK3 in convection-diffusion problems when a large CFL number is taken.","abstract_html":"This study investigates the high resolution time-limiter schemes for conservation laws. These schemes are proposed (K.Duraisamy, J.D.Baeder, J-G Liu, 2003) to enhance the stability of high order implicit time marching when the time step is beyond the original TVD limit. The improved stability is realized by taking local convex combination of a higher order oscillatory method (accurate mode) with a first order unconditionally TVD method (stable mode). The application of time-limiters, which detects the local smoothness, enables the self-adjusting switch between different modes. One of the main aspects of this work is employing time-limiters to improve the stability of the strongly S-stable DIRK3 scheme, which is shown to be non-SSP and thus may generate strong oscillations in non-smooth problems. The new Limited-DIRK3 scheme (L-DIRK3) is proposed. For convenience of applications to systems of equations, we also propose a new and convenient construction of time-limiter, which allows an arbitrary choice of reference quantity with minimal computation cost. Another innovation of our work is the extension of time-limiter schemes to multi-dimensional problems and convection-diffusion problems. The numerical results for one- and two-dimensional problems confirm that the L-DIRK3 scheme generate high resolution and less oscillatory solutions under large time step. Particularly, the L-DIRK3 scheme shows a clear improvement against the original DIRK3 in convection-diffusion problems when a large CFL number is taken.","abstract_has_math":false,"creators":["Lu, Jingcheng"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Aerospace Engineering","school":null,"contributors":[],"advisors":["Baeder, James D"],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022","date_published":"2022","updated_at":"2026-07-24T03:02:13Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.13016/a3ng-ofcu"],"render_values":[{"text":"https://doi.org/10.13016/a3ng-ofcu","href":"https://doi.org/10.13016/a3ng-ofcu","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1903/29312","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Baeder, James D"]},{"key":"dc:contributor.department","label":"Department","values":["Aerospace Engineering"]},{"key":"dc:creator","label":"Author","values":["Lu, Jingcheng"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2022-09-27T05:35:06Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-09-27T05:35:06Z"]},{"key":"dc:date.issued","label":"Date","values":["2022"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.13016/a3ng-ofcu"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1903/29312"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This study investigates the high resolution time-limiter schemes for conservation laws. These schemes are proposed (K.Duraisamy, J.D.Baeder, J-G Liu, 2003) to enhance the stability of high order implicit time marching when the time step is beyond the original TVD limit. The improved stability is realized by taking local convex combination of a higher order oscillatory method (accurate mode) with a first order unconditionally TVD method (stable mode). The application of time-limiters, which detects the local smoothness, enables the self-adjusting switch between different modes. One of the main aspects of this work is employing time-limiters to improve the stability of the strongly S-stable DIRK3 scheme, which is shown to be non-SSP and thus may generate strong oscillations in non-smooth problems. The new Limited-DIRK3 scheme (L-DIRK3) is proposed. For convenience of applications to systems of equations, we also propose a new and convenient construction of time-limiter, which allows an arbitrary choice of reference quantity with minimal computation cost. Another innovation of our work is the extension of time-limiter schemes to multi-dimensional problems and convection-diffusion problems. The numerical results for one- and two-dimensional problems confirm that the L-DIRK3 scheme generate high resolution and less oscillatory solutions under large time step. Particularly, the L-DIRK3 scheme shows a clear improvement against the original DIRK3 in convection-diffusion problems when a large CFL number is taken."]},{"key":"dc:title","label":"Title","values":["High Resolution Time-Limiter Schemes for Conservation Laws"]}]}],"canonical_facts":{"dc:contributor.advisor":["Baeder, James D"],"dc:contributor.department":["Aerospace Engineering"],"dc:creator":["Lu, Jingcheng"],"dc:date.accessioned":["2022-09-27T05:35:06Z"],"dc:date.available":["2022-09-27T05:35:06Z"],"dc:date.issued":["2022"],"dc:description.abstract":["This study investigates the high resolution time-limiter schemes for conservation laws. These schemes are proposed (K.Duraisamy, J.D.Baeder, J-G Liu, 2003) to enhance the stability of high order implicit time marching when the time step is beyond the original TVD limit. The improved stability is realized by taking local convex combination of a higher order oscillatory method (accurate mode) with a first order unconditionally TVD method (stable mode). The application of time-limiters, which detects the local smoothness, enables the self-adjusting switch between different modes. One of the main aspects of this work is employing time-limiters to improve the stability of the strongly S-stable DIRK3 scheme, which is shown to be non-SSP and thus may generate strong oscillations in non-smooth problems. The new Limited-DIRK3 scheme (L-DIRK3) is proposed. For convenience of applications to systems of equations, we also propose a new and convenient construction of time-limiter, which allows an arbitrary choice of reference quantity with minimal computation cost. Another innovation of our work is the extension of time-limiter schemes to multi-dimensional problems and convection-diffusion problems. The numerical results for one- and two-dimensional problems confirm that the L-DIRK3 scheme generate high resolution and less oscillatory solutions under large time step. Particularly, the L-DIRK3 scheme shows a clear improvement against the original DIRK3 in convection-diffusion problems when a large CFL number is taken."],"dc:identifier":["https://doi.org/10.13016/a3ng-ofcu"],"dc:identifier.uri":["http://hdl.handle.net/1903/29312"],"dc:language.iso":["en"],"dc:title":["High Resolution Time-Limiter Schemes for Conservation Laws"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T03:02:13Z"}