Local time stepping for the shallow water equations in MPAS-Ocean

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.