DMS Applied Mathematics Seminar

Speaker: Rihui Lan, University of South Carolina

Title: High-Order Multirate Explicit Time-Stepping Schemes for the Baroclinic-Barotropic Split Dynamics in Primitive Equations 

Abstract: In order to treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive equations for ocean modeling. Based on the framework of strong stability-preserving Runge-Kutta  approach, we propose two high-order  multirate  explicit time-stepping schemes (SSPRK2-SE and SSPRK3-SE) for the resulting split system in this paper. The  proposed schemes allow for a large time step  to be used for  the three-dimensional  baroclinic (slow) mode and a small time step for the two-dimensional barotropic (fast)  mode,  in which each of the two mode solves just need to satisfy their respective CFL conditions for numerical stability. Specifically, at each time step, the  baroclinic velocity is first computed  by advancing the baroclinic mode and fluid thickness of the system with the large time-step  and the assistance of  some intermediate approximations of the baroctropic mode obtained by substepping with the small time step; then the barotropic velocity is corrected by using  the small time step to re-advance the barotropic mode under an improved barotropic forcing produced by interpolation of the forcing terms from the preceding baroclinic mode solves; lastly, the fluid thickness is updated by coupling the baroclinic and barotropic velocities. Additionally, numerical inconsistencies on the discretized sea surface height caused by the mode splitting  are  relieved  via a reconciliation process with carefully calculated flux deficits. Two benchmark tests from the "MPAS-Ocean" platform are  carried out to numerically demonstrate  the performance and parallel scalability of the proposed SSPRK-SE schemes.