Abstract This paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproduction of the fast inertia-gravity waves. The accuracy of inertia-gravity waves reproduction is close to that of the explicit time-integration scheme. The computational efficiency of the proposed exponential semi-Lagrangian scheme is somewhat lower than the efficiency of semi-implicit semi-Lagrangian scheme, but significantly higher than the efficiency of explicit, semi-implicit, and exponential Eulerian schemes.

中文翻译：

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立方体网格上浅水方程的半拉格朗日指数时间积分法

摘要 本文提出了矩阵指数法与半拉格朗日法相结合的浅水方程在球面上的时间积分方法。显示了所开发方案的二阶精度。使用浅水模型的标准测试问题验证指数半拉格朗日方案与立方体网格上的空间近似相结合。所开发的方案在慢变流分量再现的准确性上与传统的半隐式半拉格朗日方案一样好，并且在快速惯性重力波的再现方面明显更好。惯性重力波再现的精度接近显式时间积分方案的精度。