Optimized Local Time-Stepping for the Ocean and Atmosphere
The lower plot shows the sea-surface height solution at a given tidal gauge as produced by three different time-stepping methods; SplitFB-LTS produces a qualitatively equivalent solution to the other two methods (note that the orange and green curves are under the red curve) in one tenth the time. The upper figure shows a breakdown of the different sources of speedup within the SplitFB-LTS algorithm.
Image by Jeremy Lilly, LANL
We developed and implemented a new local time-stepping (LTS) scheme, optimized for equations relevant to ocean and atmosphere modeling. This scheme, SplitFB-LTS was shown to model storm surge caused by Hurricane Sandy with a speedup of more than 10x in MPAS-Ocean.
The DOE ocean model MPAS-Ocean uses unstructured grids of variable spatial resolution; one would like to run simulations with only certain areas of the globe highly resolved. The computational efficiency obtained by SplitFB-LTS allows simulations on such meshes to run faster at higher resolutions.
The size of the time-step that can be used by explicit time-stepping schemes depends on the speed of the problem dynamics and the size of the spatial discretization. This means that the size of the admittable time-step can vary greatly in space, especially when considering meshes of variable spatial resolution. Local time-stepping (LTS) schemes provide an answer to this problem by allowing time-steps of different sizes depending on local conditions.
Building on previous work, we developed a new LTS scheme called SplitFB-LTS, optimized specifically for the shallow water equations. We then implemented this scheme in MPAS-Ocean for single-layer configurations and used it to model the storm surge caused by Hurricane Sandy in Delaware Bay. Doing this, we showed that SplitFB-LTS is up to 10 times faster in terms of computational time than the previous MPAS-Ocean default while maintaining solution quality.