Application of the Synchronized B-Grid Staggering for Solution of the Shallow-Water Equations on the Spherical Icosahedral Grid
Application of the Synchronized B-Grid Staggering for Solution of the Shallow-Water Equations on the Spherical Icosahedral Grid
复制标题
同步B网格交错在球形二十面体网格浅水方程求解中的应用
DOI：
10.1175/mwr-d-18-0304.1
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发表时间：
2019
影响因子：
3.2
通讯作者：
Miura Hiroaki
中科院分区：
文献类型：
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作者：
石原采佳;遠藤友随;菱川明栄;松山洋道 宮崎州正;Miura Hiroaki
在球面二十面体网格上发展了一个六角同步B网格（SB网格）的浅水模式。SB网格采用与ZM网格相同的变量安排，但不受ZM网格的计算模式问题的影响，因为通过非线性项排除了速度场的额外自由度中的相互作用。为了更好地表示地转平衡，一个二次重建的流体高度内的六边形/五边形细胞被用来配置梯度的二阶精度。当非地转运动比地转运动更占优势时，就会产生小尺度的噪声。为了防止速度场的解耦，增加了高粘度以迫使彼此相邻的速度同步演变。进行了一些标准试验来检验SB网格浅水模型。该模型是几乎二阶精度，如果初始条件和表面形貌是光滑的，如果高粘度的影响是小的。SB-网格模式在稳态地转平衡流试验中的误差模收敛性上级C-网格模式，而在孤立山脉流试验中的总能量守恒性则不如C-网格模式。SB-网格模型的优点在于，精度和稳定性对是否应用网格优化都是弱敏感的。SB网格是传统A网格的一种有吸引力的替代方案，并且在球面二十面体网格上与C网格竞争。
A shallow-water model using the hexagonal synchronized B grid (SB grid) is developed on the spherical icosahedral grid. The SB grid adopts the same variable arrangement as the ZM grid, but does not suffer from a computational mode problem of the ZM grid since interactions in the extra degrees of freedom of velocity fields through the nonlinear terms are excluded. For better representations of the geostrophic balance, a quadratic reconstruction of fluid height inside hexagonal/pentagonal cells is used to configure the gradient with the second-order accuracy. When nongeostrophic motions are more dominant than geostrophic ones, smaller-scale noises arise. To prevent a decoupling of the velocity fields, a hyperviscosity is added to force velocities adjacent to each other to evolve synchronously. Some standard tests are performed to examine the SB-grid shallow-water model. The model is almost second-order accurate if both the initial conditions and the surface topography are smooth and if the influence of the hyperviscosity is small. The SB-grid model is superior to a C-grid model regarding the convergence of error norms in a steady-state geostrophically balanced flow test, while it is inferior to that concerning conservation of total energy in a case of flow over an isolated mountain. An advantage of the SB-grid model is that both accuracy and stability are weakly sensitive to whether a grid optimization is applied or not. The SB grid is an attractive alternative to the conventional A grid and is competitive with the C grid on the spherical icosahedral grid.