Viscoelastic Fluid Modeling for Geophysical Applications in an Eulerian Framework

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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2026

Author dc:creator

• Pueschel, Aaron

Chair dc:contributor.committeechair

• Rudi, Johann

Committee members dc:contributor.committeemember

• De Sturler, Eric
• Roy, Christopher John

• Viscoelastic fluids
• Eulerian framework
• Finite element methods
• Newton methods
• Weissenberg number
• Computational rheology
• Continuum mechanics
• Geophysical flows
• Method of Manufactured Solutions

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:45354

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/140844