We assess the performance of a set of local time-stepping schemes for the shallow water equations implemented in the global ocean model MPAS-Ocean. The availability of local time-stepping tools is of major relevance for ocean codes such as MPAS-Ocean, which rely on a multi-resolution approach to perform regional grid refinement, for instance in proximity of the coast. In presence of variable resolution, the size of the time-step of explicit numerical integrators is bounded above by the size of the smallest cell on the grid, according to the Courant-Friedrichs-Lewy (CFL) condition. This constraint means that the time-step size used in low resolution regions must be the same as the one used in high resolution regions, resulting in an unnecessary computational effort. Local time-stepping, on the other hand, allows one to select different time-step sizes according to local, rather than global, CFL conditions, resulting in a more tailored integration process and reduced computational times. The present work is a preliminary but necessary effort aimed at paving the way for a more comprehensive work on local time-stepping for the primitive equation set with realistic geography.

中文翻译：

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MPAS-Ocean 中浅水方程的本地时间步长

我们评估了在全球海洋模型 MPAS-Ocean 中实施的浅水方程的一组局部时间步进方案的性能。本地时间步长工具的可用性与 MPAS-Ocean 等海洋代码具有重要意义，这些代码依赖于多分辨率方法来执行区域网格细化，例如在海岸附近。根据 Courant-Friedrichs-Lewy (CFL) 条件，在存在可变分辨率的情况下，显式数值积分器的时间步长的大小受网格上最小单元格大小的限制。这一约束意味着低分辨率区域中使用的时间步长必须与高分辨率区域中使用的时间步长相同，从而导致不必要的计算工作。另一方面，本地时间步进，允许人们根据本地而不是全局 CFL 条件选择不同的时间步长，从而实现更量身定制的集成过程并减少计算时间。目前的工作是一项初步但必要的工作，旨在为更全面的工作铺平道路，为具有现实地理的原始方程组进行本地时间步进。