{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/140844"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/140844","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Viscoelastic Fluid Modeling for Geophysical Applications in an Eulerian Framework","abstract":"Geological processes in the Earth's lithosphere and upper mantle exhibit elastic behavior on short timescales and viscous behavior on long timescales, motivating the use of viscoelastic models for intermediate regimes. Such models are essential for capturing both stress accumulation and permanent deformation but are highly nonlinear and numerically challenging. Classical approaches in geophysical viscoelastic modeling often favor Lagrangian or mixed Eulerian--Lagrangian frameworks, which can provide high physical fidelity at the cost of increased computational complexity. In this work, we develop viscoelastic models within a fully Eulerian framework, derived from continuum mechanics principles under the assumptions of incompressible, creeping flow. The resulting system of nonlinear partial differential equations resembles a Stokes-like formulation coupled to a Maxwell viscoelastic constitutive relation. Material objectivity is enforced through the Jaumann (Corotational) time derivative, whose numerical behavior is examined and compared with related formulations from classical viscoelastic fluid modeling. Material failure is incorporated into the models through nonlinear yielding via the von Mises yield criterion. The resulting nonlinear systems are solved using semi-implicit time integration and Newton's method. Numerical verification and validation, including the method of manufactured solutions, reveal challenges in achieving mesh-convergent solutions under uniform refinement. Finally, we compare the proposed models against classical viscoelastic benchmark problems, providing insight into the effects of modeling and numerical choices in Eulerian geophysical viscoelasticity.","abstract_html":"Geological processes in the Earth's lithosphere and upper mantle exhibit elastic behavior on short timescales and viscous behavior on long timescales, motivating the use of viscoelastic models for intermediate regimes. Such models are essential for capturing both stress accumulation and permanent deformation but are highly nonlinear and numerically challenging. Classical approaches in geophysical viscoelastic modeling often favor Lagrangian or mixed Eulerian--Lagrangian frameworks, which can provide high physical fidelity at the cost of increased computational complexity. In this work, we develop viscoelastic models within a fully Eulerian framework, derived from continuum mechanics principles under the assumptions of incompressible, creeping flow. The resulting system of nonlinear partial differential equations resembles a Stokes-like formulation coupled to a Maxwell viscoelastic constitutive relation. Material objectivity is enforced through the Jaumann (Corotational) time derivative, whose numerical behavior is examined and compared with related formulations from classical viscoelastic fluid modeling. Material failure is incorporated into the models through nonlinear yielding via the von Mises yield criterion. The resulting nonlinear systems are solved using semi-implicit time integration and Newton's method. Numerical verification and validation, including the method of manufactured solutions, reveal challenges in achieving mesh-convergent solutions under uniform refinement. Finally, we compare the proposed models against classical viscoelastic benchmark problems, providing insight into the effects of modeling and numerical choices in Eulerian geophysical viscoelasticity.","abstract_has_math":false,"creators":["Pueschel, Aaron"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Rudi, Johann"],"committee_members":["De Sturler, Eric","Roy, Christopher John"],"year":2026,"date_issued":"2026-01-15","date_published":"2026-01-15","updated_at":"2026-07-22T22:20:18Z","subjects":["Viscoelastic fluids","Eulerian framework","Finite element methods","Newton methods","Weissenberg number","Computational rheology","Continuum mechanics","Geophysical flows","Method of Manufactured Solutions"],"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:45354"],"render_values":[{"text":"vt_gsexam:45354","href":null,"code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10919/140844","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Rudi, Johann"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["De Sturler, Eric","Roy, Christopher John"]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Pueschel, Aaron"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2026-01-16T09:01:03Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-01-16T09:01:03Z"]},{"key":"dc:date.issued","label":"Date","values":["2026-01-15"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"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":["Viscoelastic fluids","Eulerian framework","Finite element methods","Newton methods","Weissenberg number","Computational rheology","Continuum mechanics","Geophysical flows","Method of Manufactured Solutions"]}]},{"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:45354"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10919/140844"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Geological processes in the Earth's lithosphere and upper mantle exhibit elastic behavior on short timescales and viscous behavior on long timescales, motivating the use of viscoelastic models for intermediate regimes. Such models are essential for capturing both stress accumulation and permanent deformation but are highly nonlinear and numerically challenging. Classical approaches in geophysical viscoelastic modeling often favor Lagrangian or mixed Eulerian--Lagrangian frameworks, which can provide high physical fidelity at the cost of increased computational complexity. In this work, we develop viscoelastic models within a fully Eulerian framework, derived from continuum mechanics principles under the assumptions of incompressible, creeping flow. The resulting system of nonlinear partial differential equations resembles a Stokes-like formulation coupled to a Maxwell viscoelastic constitutive relation. Material objectivity is enforced through the Jaumann (Corotational) time derivative, whose numerical behavior is examined and compared with related formulations from classical viscoelastic fluid modeling. Material failure is incorporated into the models through nonlinear yielding via the von Mises yield criterion. The resulting nonlinear systems are solved using semi-implicit time integration and Newton's method. Numerical verification and validation, including the method of manufactured solutions, reveal challenges in achieving mesh-convergent solutions under uniform refinement. Finally, we compare the proposed models against classical viscoelastic benchmark problems, providing insight into the effects of modeling and numerical choices in Eulerian geophysical viscoelasticity."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["Geological processes in the Earth's lithosphere and upper mantle behave like elastic solids over short timescales and flow like viscous fluids over long timescales. Accurately modeling this intermediate, viscoelastic behavior is essential for understanding how stresses build up and are released, such as during subduction and earthquakes. In this work, we derive and implement a geophysically realistic model for viscoelastic flow using techniques adapted from classical computational fluid dynamics. The model also accounts for material failure through established physical criteria. We solve the resulting models numerically and assess their accuracy and robustness using verification tests and established benchmark problems. This work contributes to ongoing efforts to develop efficient and reliable tools for modeling viscoelastic processes in the Earth."]},{"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":["Viscoelastic Fluid Modeling for Geophysical Applications in an Eulerian Framework"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Rudi, Johann"],"dc:contributor.committeemember":["De Sturler, Eric","Roy, Christopher John"],"dc:contributor.department":["Mathematics"],"dc:creator":["Pueschel, Aaron"],"dc:date.accessioned":["2026-01-16T09:01:03Z"],"dc:date.available":["2026-01-16T09:01:03Z"],"dc:date.issued":["2026-01-15"],"dc:description.abstract":["Geological processes in the Earth's lithosphere and upper mantle exhibit elastic behavior on short timescales and viscous behavior on long timescales, motivating the use of viscoelastic models for intermediate regimes. Such models are essential for capturing both stress accumulation and permanent deformation but are highly nonlinear and numerically challenging. Classical approaches in geophysical viscoelastic modeling often favor Lagrangian or mixed Eulerian--Lagrangian frameworks, which can provide high physical fidelity at the cost of increased computational complexity. In this work, we develop viscoelastic models within a fully Eulerian framework, derived from continuum mechanics principles under the assumptions of incompressible, creeping flow. The resulting system of nonlinear partial differential equations resembles a Stokes-like formulation coupled to a Maxwell viscoelastic constitutive relation. Material objectivity is enforced through the Jaumann (Corotational) time derivative, whose numerical behavior is examined and compared with related formulations from classical viscoelastic fluid modeling. Material failure is incorporated into the models through nonlinear yielding via the von Mises yield criterion. The resulting nonlinear systems are solved using semi-implicit time integration and Newton's method. Numerical verification and validation, including the method of manufactured solutions, reveal challenges in achieving mesh-convergent solutions under uniform refinement. Finally, we compare the proposed models against classical viscoelastic benchmark problems, providing insight into the effects of modeling and numerical choices in Eulerian geophysical viscoelasticity."],"dc:description.abstractgeneral":["Geological processes in the Earth's lithosphere and upper mantle behave like elastic solids over short timescales and flow like viscous fluids over long timescales. Accurately modeling this intermediate, viscoelastic behavior is essential for understanding how stresses build up and are released, such as during subduction and earthquakes. In this work, we derive and implement a geophysically realistic model for viscoelastic flow using techniques adapted from classical computational fluid dynamics. The model also accounts for material failure through established physical criteria. We solve the resulting models numerically and assess their accuracy and robustness using verification tests and established benchmark problems. This work contributes to ongoing efforts to develop efficient and reliable tools for modeling viscoelastic processes in the Earth."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:45354"],"dc:identifier.uri":["https://hdl.handle.net/10919/140844"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Viscoelastic fluids","Eulerian framework","Finite element methods","Newton methods","Weissenberg number","Computational rheology","Continuum mechanics","Geophysical flows","Method of Manufactured Solutions"],"dc:title":["Viscoelastic Fluid Modeling for Geophysical Applications in an Eulerian Framework"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:18Z"}