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在本文中引进了圆弧元素,使网格区域和南、北半球完全重合,导出了构造Arakawa格式的通用方法,并且证明了导出的Arakawa格式推广是真正严格满足三个守恒关系式的。本文还证明了此格式在网格结点上具有O(h)的局部逼近误差。引进圆弧元素的方法无论对求解原始方程或是过滤方程都具有实际意义。
In this paper, a circular element is introduced to completely overlap the grid area with the northern and southern hemispheres, and a general method of constructing the Arakawa scheme is derived. It is also proved that the generalized Arakawa scheme strictly satisfies the three conservation equations. The paper also proves that this format has the local approximation error of O (h) on the mesh nodes. The method of introducing arc elements has practical significance for solving the original equation or the filtering equation.