Numerical Simulations of Viscoelastic Flows Using the Discontinuous Galerkin Method

In this work, we develop a method for solving viscoelastic fluid flows using the Navier-Stokes equations coupled with the Oldroyd-B model. We solve the Navier-Stokes equations in skew-symmetric form using the mixed finite element method, and we solve the Oldroyd-B model using the discontinuous Galerkin method. The Crank-Nicolson scheme is used for the temporal discretization of the Navier-Stokes equations in order to achieve a second-order accuracy in time, while the optimal third-order total-variation diminishing Runge-Kutta scheme is used for the temporal discretization of the Oldroyd-B equation. The overall accuracy in time is therefore limited to second-order due to the Crank-Nicolson scheme; however, a third-order Runge-Kutta scheme is implemented for greater stability over lower order Runge-Kutta schemes. We test our numerical method using the 2D cavity flow benchmark problem and compare results generated with those found in literature while discussing the influence of mesh refinement on suppressing oscillations in the polymer stress.

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

2021

Author dc:creator

• Burleson, John Taylor

Chair dc:contributor.committeechair

• Yue, Pengtao

Committee members dc:contributor.committeemember

• Wapperom, Peter
• Iliescu, Traian

• viscoelastic fluids
• Oldroyd-B model
• Finite element method
• discontinuous Galerkin method
• cavity flow

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:32129

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/104869