1 research outputs found
Preconditioned solenoidal basis method for incompressible fluid flows
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