Conservative Explicit Local Timestepping Schemes for the Shallow Water Equations
In this talk we present high order explicit local timestepping (LTS) schemes for the shallow water equations. The system is discretized in space by a C grid staggering method, namely the TRiSK scheme adopted in MPAS Ocean, a global ocean model with the capability of resolving multiple resolutions within a single simulation. The time integration is designed based on the strong stability preserving Runge Kutta (SSPRK) methods, but different time step sizes can be used in different regions of the domain through the coupling of coarsefine time discretizations on the interfaces, and are only restricted by respective local CFL conditions. The proposed LTS schemes are of predictor corrector type in which the predictors are constructed based on Taylor series expansions and SSPRK stepping algorithms. The schemes preserve some important physical quantities in the discrete sense, such as exact conservation of the mass and potential vorticity and conservation of the total energy within time truncation errors. Moreover, they inherit the natural parallelism of the original explicit global timestepping schemes. Extensive numerical tests are also presented to demonstrate the performance of the proposed algorithms.
在线报告：腾讯会议 ID:518 105 482 密码：2020