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dc.contributor.authorPanuelos, Jonathan
dc.date.accessioned2021-01-21 17:49:26 (GMT)
dc.date.available2021-01-21 17:49:26 (GMT)
dc.date.issued2021-01-21
dc.date.submitted2021-01-12
dc.identifier.urihttp://hdl.handle.net/10012/16716
dc.description.abstractStandard fluid simulators often apply operator splitting to independently solve for pressure and viscous stresses. This decoupling, however, induces incorrect free surface boundary conditions. Such methods are unable to simulate various fluid phenomena reliant on the balance of pressure and viscous stresses, such as the liquid rope coil instability exhibited by honey. Unsteady Stokes solvers, when used as a sub-component of Navier-Stokes, retain coupling between pressure and viscosity, and are thus able to resolve these behaviours. The simultaneous application of stress and pressure terms, however, creates much larger, and thus more computationally expensive, systems than the standard decoupled approach. To accelerate solving the unsteady Stokes problem, we propose a reduced fluid model wherein interior regions are represented with incompressible polynomial vector fields. Sets of standard grid cells are consolidated into super-cells, each of which are modelled using only 26 degrees of freedom. We demonstrate that the reduced field must necessarily be at least quadratic, with the affine model being unable to capture viscous forces. We reproduce the liquid rope coiling instability, as well as other simulated examples, to show that our reduced model provides qualitatively similar results to the full Stokes system for a smaller computational cost.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectunsteady Stokesen
dc.subjectNavier-Stokesen
dc.subjectfluid simulationen
dc.subjectviscosityen
dc.subjectspatial refinementen
dc.subjectreduced modelsen
dc.subjectcomputer graphicsen
dc.titleVariational Stokes with Polynomial Reduced Fluid Modelen
dc.typeMaster Thesisen
dc.pendingfalse
uws-etd.degree.departmentDavid R. Cheriton School of Computer Scienceen
uws-etd.degree.disciplineComputer Scienceen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws-etd.embargo.terms0en
uws.contributor.advisorBatty, Christopher
uws.contributor.affiliation1Faculty of Mathematicsen
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


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