K. Watanabe

R. Horiuchi

T. Sugimura

National Institute for Fusion Science (NIFS-Repository)

§63. Benchmark Test Using New Reduced Grid Sugimura. T. (Grad. Sci., Nagoya Univ.) Horiuchi, R. Watanabe, K. (Earth Simulator Center) vVe have been developed a non-hydrostatic atm(}-spheric global circulation simulation code by using our advanced reduced grid system (Fig.l(c)). Original Re-duced grida (Kurihara 1965) was well known as a grid system (Fig.l(a)), called Kurihara grid, which longitudal grids points decreases gradually toward the poles. In or-der to reduce computational crfors in derivatives of the approximate solution) grid aspect ratio is required to be 1.0 for any objective region. In the Kurihara grid system, there are only 4 grid points in the polar region, therefore, grid aspect ratio is 2; ~ 1.5 there. In this study, we introduce a new grid system which is divided into 6 regions, and longitudal grids points change each longitude. Thus, in this advanced Reduced grid, grid aspect· ratio near the pole region becomes 2; '" 1. 045. Because this grid system is un-structured grid, we have to have the list array and search the reference points (Fig.2(a)). However, list representation make calculation efficiency reduce. Then, we have used a 2-dimensional array in order to use no list. But the 2-dimensional array have wa.'3te area, which is white squares in Fig.2(b) and is 36.3% of whole area. To reduce the area, we use Fig.2(c) array image. This changes reduce the waste area 3.0 % of whole area. To meet the necessity of a good benchmark to test new grid system for solving the 2-dimensional shallow-water equations, Williamson et al (1992) developed a test set, containing the seven different test cases of increasing complexity. Fig.4 shows results of test case 1, which is called Advection of Cosine Bell over the Pole. This case tests the advective component in isolation. 0: is parameter of advection direction. We tests 0: = 0 ( along-equator flow), and a = 90 ( cross-pole flow) advection using finite volume method(FVM). u>. = -Uo sin>. sin <p, u¢ = -Uo cos >. (a).Kurihara grid (b ).lat-lon Reduced grid Fig. 1. Reduced grid. (c).advanced Reduced grid Fig.4 shows results of this case's h norm using a grid sys-tem of Fig.1(b) (the lat-Ion Reduced grid) and (c) (the advanced Reduced grid). Cell interface of lat-lon Re-duced grid differs from its of the advanced Reduced grid system. Initial Reduced grid coincide with latitudal and longitudalline, on the other side, the advanced Reduced grid doesn't coincide(Fig.l). In this test case, since the field is analytical nondi-vergent: the initial divergence pattern computed on the grid system will be a mesure of the accuracy of the differ-ence approximations and the grid. The cross-polar flow is a particularly suitable experimnts to validate the trun-cation error at high latitudes, because its strongest flow goes directly across the Pole. The height field after 1 step integration is presented in Fig.5. The divergence of the advanced Reduced grid is 3 order smaller than that of the lat-Ion Reduced grid. Finally, Fig.3 shows that this FVM s~heme can keep second-order accuracy. w' (a).real space array (b) 2-. (c) array dimensional. . array Image Fig. 3. scheme accu-racy. 0.04 0.04 a-9O _ =90_ ...0 o>=IJ ••• _-0.03 0.03 0.02 0.02 0.01 0.01 ',k'C.--o---c-<-, ~c-.,;",......J" "" ',;:<--;---;--t", --,c--.,;"~,, "" (b).advauced (a).lat-Ion Reduced grid grid Reduced Fig. 4. 12 norm. (a).lat-lon Reduced grid (b). advanced Reduced grid Fig. 5. 'V. V flow pattern. References 1) Y.Kurihara., Mon.Weth.Rev., 93(1965)399 2) D.L.Williamson et at., J.Comp.Phys., 102(1992)211 3) C.H.Dey., Mon.Weth.Rev., 97(1969)597 387 

Benchmark Test Using New Reduced Grid

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