An Exponential Time Differencing Time-Stepping Scheme for the Tracer Equations in MPAS-Ocean

Abstract

Exponential time differencing (ETD) methods, also known as exponential integrators, constitute a class of numerical methods for the time integration of stiff systems of differential equations. This manuscript investigates an ETD scheme for solving the tracer equations appearing in primitive equation ocean models, and shows the results obtained when such a scheme is applied within a full ocean circulation model. The main idea behind the scheme is the treatment of the vertical terms (transport and diffusion) with a matrix exponential, whereas the horizontal terms are dealt with in an explicit way. The performance of the ETD scheme is compared against that of other semi-implicit time-stepping schemes for realistic ocean configurations on quasi-uniform and variable resolution meshes.