Comparison of exponential integrators and traditional time integration schemes for the shallow water equations

The time integration scheme is probably one of the most fundamental choices in the development of an ocean model. In this paper, we investigate several time integration schemes when applied to the shallow water equations. This set of equations is accurate enough for the modeling of a shallow ocean and is also relevant to study as it is the one solved for the barotropic (i.e. vertically averaged) component of a three dimensional ocean model. We analyze different time stepping algorithms for the linearized shallow water equations. High order explicit schemes are accurate but the time step is constrained by the Courant-Friedrichs-Lewy stability condition. Implicit schemes can be unconditionally stable but, in practice lack accuracy when used with large time steps. In this paper we propose a detailed comparison of such classical schemes with exponential integrators. The accuracy and the computational costs are analyzed in different configurations.(c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

The choice of time integration scheme is crucial in the development of an ocean model. This paper investigates various time integration schemes applied to the shallow water equations. Different algorithms for time stepping in linearized shallow water equations are analyzed, and a detailed comparison between classical schemes and exponential integrators is proposed.