An optimization of the Icosahedral grid modified by spring dynamics
An optimization of the Icosahedral grid modified by spring dynamics
复制标题
弹簧动力学修正的二十面体网格的优化
DOI：
10.1006/jcph.2002.7193
复制
发表时间：
2002
影响因子：
4.1
通讯作者：
Koji Goto
中科院分区：
文献类型：
--
作者：
H. Tomita;M. Satoh;Koji Goto
我们研究了一种改进的二十面体网格的最佳形式，它是通过将弹簧动力学应用于标准的二十面体网格系统而产生的。弹簧动力学通过调节自然弹簧长度可以生成比标准二十面体网格系统更均匀的网格系统：随着自然弹簧长度变长，最大网格间隔与最小网格间隔的比值变得更接近单位。然而，当自然弹簧长度大于临界值时，弹簧动力系统不具有稳定平衡。通过将自然弹簧长度设置为临界值，我们可以得到最均匀的网格系统，这是最有效的CFL条件。本文分析了地转平衡问题[D。L.威廉姆森（Williamson）等人（1992，J. Comput. 102，211）]。由于离散系统的平衡状态与解析系统的精确解略有不同，初始误差场包括重力波模式和Rossby波模式。由于分析的结果是基于霍夫谐波分解，我们检测到Rossby和重力波模式的纬向波数为5，这是对赤道不对称。这些误差与二十面体网格结构有关。误差场中还出现了纬向波数为0的对称重力波模式。为了阐明Rossby波的演化，我们引入了发散阻尼来减少重力波模式。通过对不同网格系统下地转问题的模拟结果发现，当采用最均匀分布的网格系统时，可以最有效地消除伪Rossby波模。因此，从数值精度和计算效率的角度来看，最均匀的网格系统是最好的选择。
We have investigated an optimum form of the modified icosahedral grid that is generated by applying the spring dynamics to the standard icosahedral grid system. The spring dynamics can generate a more homogeneous grid system than the standard icosahedral grid system by tuning the natural spring lenght: as the natural spring length becomes longer, the ratio of maximum grid interval to minimum one becomes closer to unit. When the natural spring length is larger than a critical value, however, the spring dynamic system does not have a stable equilibrium. By setting the natural spring length to be the marginally critical value, we can obtain the most homogeneous grid system, which is most efficient in terms of the CFL condition. We have analyzed eigenmodes involved in the initial error of the geostrophic balance problem [test case 2 of D. L. Williamson et al. (1992, J. Comput. Phys. 102, 211)]. Since the balance state in the discrete system differs slightly from the exact solution of the analytic system, the initial error field includes both the gravity wave mode and the Rossby wave mode. As the results of the analysis are based on Hough harmonics decompositions, we detected Rossby and gravity wave modes with zonal wavenumber 5, which are asymmetric against the equator. These errors are associated with icosahedral grid structure. The symmetric gravity wave mode with zonal wavenumber 0 also appears in the error field. To clarify the evolution of Rossby waves, we introduce divergence damping to reduce the gravity wave mode. From the simulated results of the geostrophic problem with various grid systems, we found that the spuriously generated Rossby wave mode is eliminated most effectively when the most homogeneously distributed grid system is used. It is therefore, concluded that the most homogeneous grid system is the best choice from the viewpoint of numerical accuracy as well as computational efficiency.