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ArticleA modified atmospheric non-hydrostatic model on low aspect ratio grids : part II(International Meteorological Institute, 2013-06-28) Sun, Wen-Yih ; Sun, Oliver M. T. ; Tsuboki, KazuhisaSun et al. (2012) proposed a modified non-hydrostatic model (MNH), in which the left-hand side of the continuity equation is multiplied by a parameter δ(4 ≤ δ≤16 in the article) to suppress high-frequency acoustic waves. They showed that the MNH allows a longer time step than the original non-hydrostatic model (NH). The MNH is also more accurate and efficient than the horizontal explicit and vertical implicit scheme (HEVI) when the aspect ratio (Δx/Δz) is small. In addition to multiplying a parameter δ, here we propose to add a smoothing on the right-hand side of the continuity equation in the MNH to damp shortest sound waves. Linear stability analysis and non-linear model simulations show that the MNH with smoothing (henceforth abbreviated as MNHS) can use twice the time interval of the MNH while maintaining the same accuracy. The MNHS is also more accurate and efficient than HEVI when the aspect ratio is small.
ArticleA modified atmospheric non-hydrostatic model on low aspect ratio grids(International Meteorological Institute, 2012-04-17) Sun, Wen-Yih ; Sun, Oliver M. T. ; Tsuboki, KazuhisaIt is popular to use a horizontal explicit and a vertical implicit (HE-VI) scheme in the compressible nonhydrostatic (NH) model. However, when the aspect ratio becomes small, a small time-interval is required in HE-VI, because the Courant-Fredrich-Lewy (CFL) criterion is determined by the horizontal grid spacing. Furthermore, simulations from HE-VI can depart from the forward–backward (FB) scheme in NH even when the time interval is less than the CFL criterion allowed. Hence, a modified non-hydrostatic (MNH) model is proposed, in which the left-hand side of the continuity equation is multiplied by a parameter d (45d516, in this study). When the linearized MNH is solved by FB (can be other schemes), the eigenvalue shows that MNH can suppress the frequency of acoustic waves very effectively but does not have a significant impact on the gravity waves. Hence, MNH enables to use a longer time step than that allowed in the original NH. When the aspect ratio is small, MNH solved by FB can be more accurate and efficient than the NH solved by HE-VI. Therefore, MNH can be very useful to study cloud, Large Eddy Simulation (LES), turbulence, flow over complex terrains, etc., which require fine resolution in both horizontal and vertical directions.