In high‐resolution numerical weather prediction models, fast‐moving acoustic waves must be treated in a stable manner. Among the implicit–explicit (IMEX) schemes used for the solution of these models, horizontally explicit, vertically implicit (HEVI) methods show good stability and scalability on massively parallel machines. In this work, we present two classes of exponential time‐differencing (ETD) methods for atmospheric models that use a HEVI splitting strategy, one being a three‐stage method with the addition of artificial diffusion, the second based on a Strang splitting approach. The stability properties of the methods are analyzed and numerical examples are provided, which compare time‐step restrictions and cost‐to‐accuracy ratios of the new methods with those for existing approaches.

中文翻译：

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大气模型求解指数时差方案的数值分析

在高分辨率数值天气预报模型中，必须以稳定的方式对待快速移动的声波。在用于解决这些模型的隐式-显式（IMEX）方案中，水平显式，垂直式隐式（HEVI）方法在大规模并行机上显示出良好的稳定性和可伸缩性。在这项工作中，我们为使用HEVI分裂策略的大气模型提供了两种类型的指数时差（ETD）方法，一种是增加了人工扩散的三阶段方法，第二种是基于Strang分裂方法的。分析了这些方法的稳定性，并提供了数值示例，比较了新方法与现有方法的时间步长限制和成本精度比。