Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver
Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver
复制标题
使用带有多重网格求解器的矢量半拉格朗日格式对球体上的浅水方程进行积分
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
Saulo R. M. Barros
中科院分区：
文献类型：
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作者：
J. Bates;F. Semazzi;R. W. Higgins;Saulo R. M. Barros
摘要提出了一种求解球上浅水波方程的向量半拉格朗日半隐式两时间层有限差分积分格式。C网格用于空间差分。以矢量形式的动量方程的无偏中心离散化消除了极点问题，并且在可比的成本下，比以前使用旋转球坐标系的半拉格朗日有限差分格式具有更高的精度。在增加时间步长的结果的不敏感性方面，新的计划是成功的最近的谱半拉格朗日计划。此外，使用多重网格方法求解椭圆方程的位势允许有效的集成与操作计数，在高分辨率下，是较低的顺序比的情况下的谱模型。新方案的性质应允许有限差分模型与光谱模型竞争比以前更有效。
Abstract A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the, new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.