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


主講人:鞠立力,University of South Carolina 教授




內容介紹:In this talk we present 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 are presented to illustrate the performance of the proposed  algorithms.

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