Preconditioned solenoidal basis method for incompressible fluid flows

by Wang, Xue

Abstract (Summary)
This 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.
Bibliographical Information:

Advisor:Sarin, Vivek; Klappenecker, Andreas; Chen, Hamn-Ching

School:Texas A&M University

School Location:USA - Texas

Source Type:Master's Thesis

Keywords:solenoidal basis incompressible fluid flow null space divergence free


Date of Publication:12/01/2004

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