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首页> 美国政府科技报告 >Modeling, Analysis and Simulation: A Comparison of Operator and Approximate Matrix Factorization for the Shallow Water Equations in Spherical Geometry
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Modeling, Analysis and Simulation: A Comparison of Operator and Approximate Matrix Factorization for the Shallow Water Equations in Spherical Geometry

机译：建模，分析与仿真：球面几何中浅水方程算子与近似矩阵分解的比较

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摘要

The shallow water equations (SWEs) in spherical geometry provide a basic prototype for developing and testing numerical algorithms for solving the horizontal dynamics in global atmospheric circulation models. When solving the SWEsers a global ne uniform lat-lon grid, an explicit time from a severe stability restriction on the admissible step size. In a previous paper, we investigated an A- stable, linearly-implicit, third-order time integration method (Ros3), which we combined with approximate matrix factorization (AMF) to make it cost effective. In this paper, we further explore this method and we compare it to a Strang-type operator splitting method. Our main focus is on the local error of the methods, their numerical dispersion relation and their accuracy and efficiency when applied to the well-known SWEs test set. The comparison shows that Ros3 with AMF accurately presents both low and mid frequency waves. Moreover, Ros3 with AMF makes a good candidate for the efficient solution of the SWEs on a global fine lat-lon grid. In contrast, Strang splitting is not advocated, in view of its inaccuracy in the polar area and the resulting inefficiency.

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