By Ting T.C.T.
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Extra resources for Anisotropic elasticity
Similar data for Reynolds numbers of Red = 60, Red = 90, Red = 150, and Red = 180 also are shown in the figure, as well as the experimental data determined by Williamson, (plotted at effectively zero mesh spacing); it is seen that the current numerical results agree quite well with the experimental values. If fi, f2, and f3 are taken to denote the computed frequencies on meshes containing 386 x 192, 192 x 96, and 128 x 64 cells, respectively, then the limiting value fo, corresponding to zero mesh spacing, is given by when the leading error in the Richardson extrapolation is assumed to be proportional to the square of the mesh size.
That, in the same regime, K, does not scale as maximum K, scales as T - ~ / Note r - 4 / 5This . is because the position of the maxima do not coincide. This regime corresponds to an approach to a vertical tangent that occurs just before the interface turns over. If the interface were symmetric about the vertical tangent, its shape would be a cusp. It is not symmetric and the asymmetry gives it a modified '2'-shape rather than cusp-shape (see figure 4). Prior to the -215 regime, maximum K , apparently scales as T-l.
Finally, we present results computed on ultrafine grids containing 384 x 192 cells in order to demonstrate convergence of the solution with spatial mesh size. The dimensionless frequency is plotted in Fig. 6 as a function of the square of the mesh spacing for this grid and for two coarser grids: the standard grid containing 192 x 96 cells and a coarser grid containing 128 x 64 cells. Results on all grids were computed using A? 02, so the timestepping error is assumed to be negligibly small. Richardson extrapolation6 is used to predict the limiting value of the frequency corresponding to zero mesh spacing.
Anisotropic elasticity by Ting T.C.T.