摘要:非跳点网格在模式动力—物理过程的耦合方面具有独特的优势，但是由于二阶精度差分方案下非跳点网格频散误差较大而很少被使用于数值天气预报模式。随着近年来数值模式计算精度的不断提高，非跳点网格在频散关系方面的计算误差是否会发生变化还有待研究。本文在高阶精度差分格式下通过浅水波方程对跳点网格和非跳点网格的频散关系进行理论分析和数值试验，主要得到以下结论：（1）在低波数区跳点网格的频散关系基本不随计算精度的提高而变化，但是非跳点网格下的频散关系则随着计算精度的提高而更加接近真实解。在四阶精度下，非跳点网格的频散关系已经非常接近跳点网格。（2）差分精度提高以后，在高波数区非跳点网格仍然存在频率极大值，而且极值中心随着计算精度的提高而逐渐向更高波数区移动。跳点网格在计算精度提高以后高波数区的频率仍然随波数单调增加，且更接近真实解。（3）在高阶精度非跳点网格模拟试验的基础上，结合高阶扩散项对高频短波进行滤除，可以得到与二阶精度跳点网格相接近的模拟结果。总之，在高阶精度有限差分方案下利用非跳点网格构造模式动力框架是一种比较可行的做法。
关键词:非跳点网格/
高阶精度/
有限差分/
浅水波方程
Abstract:Although the nonstaggered grid has better physical consistency than the staggered grid, it is still not widely used, mainly because of its poor accuracy for simulating the geostrophic adjustment process under the second-order accuracy difference scheme. However, for higher-order finite-difference schemes, the validity of the above conclusion is still unknown. In this paper, we present a theoretical analysis and a numerical test for shallow water equation under high-order difference schemes. The analysis and test results are as follows. (1) For a low wavenumber, the dispersion of a staggered grid does not change with the accuracy of the difference scheme, while the dispersion of nonstaggered grid is significantly improved, and the dispersion of both grids become very close under the fourth-order scheme. (2) The maximum frequency of nonstaggered grid still exists under high-order difference schemes, and it moves toward a higher wavenumber as the accuracy of the difference scheme increases. The frequency of the staggered grid monotonically increases with the wavenumber and gets closer to the real solution under high-order difference schemes. (3) When the high-frequency noise is removed by explicitly adding a diffusion term, the pros and cops to grid staggering choices diminish with high-order schemes. In general, the nonstaggered grid is an attractive choice for the discretization of the dynamical frame in numerical models under high-order difference scheme.
Key words:Nonstaggered grid/
High order accuracy/
Finite difference/
Shallow water equation
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