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Numerical Simulations of Viscoelastic Flows Using the Discontinuous Galerkin Method

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dc.contributor.authorBurleson, John Tayloren
dc.contributor.committeechairYue, Pengtaoen
dc.contributor.committeememberWapperom, Peteren
dc.contributor.committeememberIliescu, Traianen
dc.contributor.departmentMathematicsen
dc.date.accessioned2021-08-31T08:00:14Zen
dc.date.available2021-08-31T08:00:14Zen
dc.date.issued2021-08-30en
dc.description.abstractIn 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.en
dc.description.abstractgeneralViscoelastic fluids are a type of non-Newtonian fluid of great importance to the study of fluid flows. Such fluids exhibit both viscous and elastic behaviors. We develop a numerical method to solve the partial differential equations governing viscoelastic fluid flows using various finite element methods. Our method is then validated using previous numerical results in literature.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:32129en
dc.identifier.urihttp://hdl.handle.net/10919/104869en
dc.language.isoenen
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectviscoelastic fluidsen
dc.subjectOldroyd-B modelen
dc.subjectFinite element methoden
dc.subjectdiscontinuous Galerkin methoden
dc.subjectcavity flowen
dc.titleNumerical Simulations of Viscoelastic Flows Using the Discontinuous Galerkin Methoden
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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