Parallel Exponential Time Differencing Methods for Geophysical Flow Simulations

TL;DR

This paper explores the application of parallel exponential time differencing methods to improve the efficiency of geophysical flow simulations in ocean models, demonstrating their potential through benchmark tests.

Contribution

It introduces new parallel ETD methods tailored for ocean models and shows their effectiveness in increasing simulation efficiency over traditional techniques.

Findings

ETD methods enable larger time steps than explicit methods.

Parallel ETD methods show promising performance in benchmark tests.

Potential for real-world geophysical flow simulation improvements.

Abstract

Two ocean models are considered for geophysical flow simulations: the multi-layer shallow water equations and the multi-layer primitive equations. For the former, we investigate the parallel performance of exponential time differencing (ETD) methods, including exponential Rosenbrock-Euler, ETD2wave, and B-ETD2wave. For the latter, we take advantage of the splitting of barotropic and baroclinic modes and propose a new two-level method in which an ETD method is applied to solve the fast barotropic mode. These methods could improve the computational efficiency of numerical simulations because ETD methods allow for much larger time step sizes than traditional explicit time-stepping techniques that are commonly used in existing computational ocean models. Several standard benchmark tests for ocean modeling are performed and comparison of the numerical results demonstrate a great potential of applying the parallel ETD methods for simulating real-world geophysical flows.