| Summary: | 碩士 === 國立臺灣大學 === 機械工程學系研究所 === 86 === The two-dimensional incompressible Navier-Stokes equations are solved by
using the conforming Legendre spectral element method as well as the splitting
technique. Three different pressure boundary conditions are employed, the in-
viscid one, the viscous one, and the one that enforces incompressibility at the
boundaries by taking advantage of numerical Green functions. This study
attempts to investigate the so-called splitting error due to the splitting
technique and the improper pressure boundary conditions.
The research shows that when flows involves with no inflow/
outflow boundaries,
the viscous-pressure-boundary-condition scheme and the Green-function technique
do have a spectral accuracy, but the inviscid scheme does not.
This implies that
the inviscid pressure boundary condition causes too large a splitting error
which cannot be overcome by simply increasing the spatial resolution. The
research also shows that the incompressibility constraints is better sustained
near boundaries but worse inside the flow when Green-function
scheme is applied,
compared to the viscous one.
Flows with inflow/outflow boundaries are simulated as well, although the
inflow/outflow velocity and pressure boundary conditions, the proper size of
the simulated domain, and the spatial resolution are not really well considered
and need much more exploration. Several issues concerning the Green-function
scheme are unearthed. First, to be numerically stable, the Green-function
scheme must employ a further exit. Secondly, the induced splitting error is
more sensitive to the initial and boundary conditions. Finally, the shape of
the element including a corner has to be rectangular in order to prevent the
contamination of the incorrect pressure at the corner from the entire flow.
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