News & Events
Speaker:Ju Lili, Professor, University of South Carolina
Date:Dec. 3, 2021
Location:Tencent Meeting, ID: 570 424 940, Code: 211203
Sponsor:School of Mathematics, Shandong University
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. We propose second and third order multirate explicit time-stepping schemes for such split system based on the strong stability-preserving Runge-Kutta (SSPRK) framework. Our method allows for a large time step to be used for advancing the three-dimensional (slow) baroclinic mode and a small-time step for the two-dimensional (fast) barotropic mode, so that each of the two mode solves only need satisfy their respective CFL condition to maintain numerical stability.
It is well known that the SSPRK method achieves high-order temporal accuracy by utilizing a convex combination of forward-Euler steps. At each time step of our method, the baroclinic velocity is first computed by using the SSPRK scheme with the large time step, then the barotropic velocity is specially corrected by using the same SSPRK scheme with the small-time step. Finally, the fluid thickness and the sea surface height perturbation are updated by coupling the predicted baroclinic and barotropic velocities, and the inconsistency on the sea surface height caused by the mode splitting is also resolved via a reconciliation process with carefully calculated flux deficits and velocity adjustments. Two benchmark tests drawn from the “MPAS-Ocean” platform are used to numerically demonstrate the accuracy and parallel performance of the proposed schemes.
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