The “Cubed Sphere”
The “Cubed Sphere”
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DOI：
10.1006/jcph.1996.0047
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发表时间：
1996-03
影响因子：
4.1
通讯作者：
C. Ronchi;R. Iacono;P. Paolucci
中科院分区：
文献类型：
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作者：
C. Ronchi;R. Iacono;P. Paolucci
提出了一种求解球面几何中偏微分方程的新网格技术。该方法是基于分解成六个相同的区域，通过投影到球面上的外切立方体的侧面获得的球体。通过选择每个区域上的坐标线为大圆弧，可以得到六个没有任何奇异性并定义相同度量的坐标系。充分利用分解的对称性，将复合网格有限差分法的一种变体应用于耦合六个网格，以高效率获得球面上偏微分方程的非常精确的数值解。这种新技术的优点是光谱和统一的经度？纬度网格点方法在串行和并行架构上的应用的上下文中讨论。我们提出了两个测试情况下的数值逼近的浅水方程在球面几何形状的结果：线性平流的余弦钟和非线性演化的Rossby？Haurwitz波后一种情况下的性能分析表明，新的方法可以提供，大量节省执行时间，数值解是准确的光谱变换方法所获得的。
A new gridding technique for the solution of partial differential equations in spherical geometry is presented. The method is based on a decomposition of the sphere into six identical regions, obtained by projecting the sides of a circumscribed cube onto a spherical surface. By choosing the coordinate lines on each region to be arcs of great circles, one obtains six coordinate systems which are free of any singularity and define the same metric. Taking full advantage of the symmetry properties of the decomposition, a variation of the composite mesh finite difference method can be applied to couple the six grids and obtain, with a high degree of efficiency, very accurate numerical solutions of partial differential equations on the sphere. The advantages of this new technique over both spectral and uniform longitude?latitude grid point methods are discussed in the context of applications on serial and parallel architectures. We present results of two test cases for numerical approximations to the shallow water equations in spherical geometry: the linear advection of a cosine bell and the nonlinear evolution of a Rossby?Haurwitz wave. Performance analysis for this latter case indicates that the new method can provide, with substantial savings in execution times, numerical solutions which are as accurate as those obtainable with the spectral transform method.