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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/3295 |
| Date | 12 April 2006 |
| Creators | Wang, Xue |
| Contributors | Sarin, Vivek |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | 383288 bytes, electronic, application/pdf, born digital |
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