Preconditioned solenoidal basis method for incompressible fluid flows
Abstract
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.
Citation
Wang, Xue (2004). Preconditioned solenoidal basis method for incompressible fluid flows. Master's thesis, Texas A&M University. Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /3295.