Multi-layer shallow water and primitive equations are commonly employed to predict geophysical flows when stratification effects are taken into account. The scientists designed and implemented parallel exponential time differencing (ETD) methods for time integration of these equations based on domain decomposition to speed up their numerical simulations. Specifically, exponential Rosenbrock-Euler, ETD2wave, and B-ETD2wave schemes are implemented for the multi-layer shallow water equations. The ETD method is also applied to solve the (fast) barotropic mode, instead of the explicit sub-stepping process currently implemented in MPAS-Ocean, within the baroclinic-barotropic splitting approach for the multi-layer primitive equations.
This work shows the great potential of applying parallel ETD methods for simulating real-world geophysical flows. First, the proposed parallel ETD methods obtain good parallel scalability for the shallow water equations and the primitive equations. Secondly, compared to existing models in MPAS-Ocean, the proposed methods can result in lower computational costs to achieve similar accuracies.
The multi-layer shallow water equations and the multi-layer primitive equations are considered for geophysical flow simulations. For the former, this study investigates the parallel performance of exponential time differencing methods, including exponential Rosenbrock-Euler, ETD2wave, and B-ETD2wave. For the latter, the proposed work takes advantage of the splitting of barotropic and baroclinic modes and designs a new two-level method in which the ETD method is applied to solve the fast barotropic mode. These methods improve the computational efficiency of numerical simulations for geophysical flows because ETD methods allow for much larger time step sizes than traditional explicit time-stepping schemes popularly used in existing computational ocean models. Several benchmark tests for ocean modeling are carried out to demonstrate the performance and parallel scalability of the proposed ETD methods.