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Here we apply this theory to spectral approximations to two-dimensional steady problems.
The generalized decomposition is shown to be useful for a wide range of problems including steady problems.
However, they face several problems, at least for steady problems which are the only cases considered here.
This computational result suggests employing fine spatial resolution rather than fine temporal resolution would be effective for analyzing steady problems with the support.
Both for steady problems and for sub-iterations within unsteady problems, a globally coupled system of residual equations is solved by Newton's method.
We demonstrate the validity of this approach for steady problems (Poiseuille flow, lid-driven cavity) as well as for the unsteady oscillating flow over a flat plate.
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This transformation has no counterpart in the corresponding steady problem.
In the present study we propose an original approach to solve the steady problem.
We plot the streamlines of velocity for the steady problem and the time-dependent problem at final time (t=6.31) in Figure 7 and Figure 8, respectively.
Figure 7 Streamlines of velocity contours for u: steady problem. Figure 8 Streamlines of velocity contours for u: time-dependent problem at final time (pmb{t=6.31}).
However, we find that the solutions of the time-dependent problem can converge to the solutions of the steady problem. Figure 5 Horizontal velocity (pmb{u_{1}}) near reentrant corner ( (pmb{x=4.0625}) ).
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