Sarin, Vivek2006-04-122017-04-072006-04-122017-04-072004-122006-04-12http://hdl.handle.net/1969.1/3295This 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.en-USsolenoidal basisincompressible fluid flownull spacedivergence freeBook