A Finite-Element Coarse-GridProjection Method for Incompressible Flows

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dc.contributor.authorKashefi, Alien
dc.contributor.committeechairStaples, Anne E.en
dc.contributor.committeememberRagab, Saaden
dc.contributor.committeememberIliescu, Traianen
dc.contributor.departmentEngineering Science and Mechanicsen
dc.date.accessioned2017-11-02T20:48:45Zen
dc.date.adate2017-05-23en
dc.date.available2017-11-02T20:48:45Zen
dc.date.issued2017-04-10en
dc.date.rdate2017-05-23en
dc.date.sdate2017-04-24en
dc.description.abstractCoarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic Poisson equations. The nonlinear equations are solved on a fine grid and the linear equations are solved on a corresponding coarsened grid. Mapping operators execute data transfer between the grids. The CGP framework is constructed upon spatial and temporal discretization schemes. This framework has been established for finite volume/difference discretizations as well as explicit time integration methods. In this article we present for the first time a version of CGP for finite element discretizations, which uses a semi-implicit time integration scheme. The mapping functions correspond to the finite-element shape functions. With the novel data structure introduced, the mapping computational cost becomes insignificant. We apply CGP to pressure correction schemes used for the incompressible Navier Stokes flow computations. This version is validated on standard test cases with realistic boundary conditions using unstructured triangular meshes. We also pioneer investigations of the effects of CGP on the accuracy of the pressure field. It is found that although CGP reduces the pressure field accuracy, it preserves the accuracy of the pressure gradient and thus the velocity field, while achieving speedup factors ranging from approximately 2 to 30. Exploring the influence of boundary conditions on CGP, the minimum speedup occurs for velocity Dirichlet boundary conditions, while the maximum speedup occurs for open boundary conditions. We discuss the CGP method as a guide for partial mesh refinement of incompressible flow computations and show its application for simulations of flow over a backward facing step and flow past a cylinder.en
dc.description.abstractgeneralCoarse Grid Projection (CGP) methodology is a new multigrid technique applicable to pressure projection methods for solving the incompressible Navier-Stokes equations. In the CGP approach, the nonlinear momentum equation is evolved on a fine grid, and the linear pressure Poisson equation is solved on a corresponding coarsened grid. Mapping operators transfer the data between the grids. Hence, one can save a considerable amount of CPU time due to reducing the resolution of the pressure filed while maintaining excellent to reasonable accuracy, depending on the level of coarsening.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-04242017-103714en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04242017-103714/en
dc.identifier.urihttp://hdl.handle.net/10919/79948en
dc.language.isoen_USen
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectSemi-implicit time integrationen
dc.subjectFinite elementsen
dc.subjectCoarse-grid projectionen
dc.subjectUnstructured gridsen
dc.subjectGeometric multigrid methodsen
dc.subjectPressure-correction schemesen
dc.titleA Finite-Element Coarse-GridProjection Method for Incompressible Flowsen
dc.typeThesisen
dc.type.dcmitypeTexten
thesis.degree.disciplineEngineering Science and Mechanicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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