E4.14 Local Time-Stepping Schemes for the SWEs

                    

Poster Title

Conservative Explicit Local Time-Stepping Schemes for the Shallow Water Equations

AuthorsLili Ju (Unlicensed)Thi Thao Phuong Hoang (Unlicensed), Wei Leng, Zhu Wang (Unlicensed)Konstantin Pieper (Unlicensed)
First AuthorLili Ju (Unlicensed)
Session TypeE3SM/Integrated Session
Session IDI3 and E4
Submission TypePoster
GroupOcean/Ice
Experiment
Poster Link




Abstract


We develop explicit local time-stepping (LTS) schemes with second and third order accuracy 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 (SSP-RK) methods, but different time step sizes can be used in different regions of the domain through the coupling of coarse-fine time discretizations on the interface 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 SSP-RK 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 time-stepping schemes. Extensive numerical tests including are presented to illustrate the performance of the proposed algorithms in accuracy, conservation ability and parallel scalability.