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dc.contributorSarin, Vivek
dc.creatorWang, Xue
dc.description.abstractThis thesis presents a preconditioned solenoidal basis method to solve the algebraic system arising from the linearization and discretization of primitive variable formulations of Navier-Stokes equations for incompressible fluid flows. The system is restricted to a discrete divergence-free space which is constructed from the incompressibility constraint. This research work extends an earlier work on the solenoidal basis method for two-dimensional flows and three-dimensional flows that involved the construction of the solenoidal basis P using circulating flows or vortices on a uniform mesh. A localized algebraic scheme for constructing P is detailed using mixed finite elements on an unstructured mesh. A preconditioner which is motivated by the analysis of the reduced system is also presented. Benchmark simulations are conducted to analyze the performance of the proposed approach.
dc.publisherTexas A&M University
dc.subjectsolenoidal basis
dc.subjectincompressible fluid flow
dc.subjectnull space
dc.subjectdivergence free
dc.titlePreconditioned solenoidal basis method for incompressible fluid flows

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