Exponential time differencing for mimetic multilayer ocean models

Abstract

A framework for exponential time discretization of the multilayer rotating shallow water equations is developed in combination with a mimetic discretization in space. The method is based on a combination of existing exponential time differencing (ETD) methods and a careful choice of approximate Jacobians. The discrete Hamiltonian structure and conservation properties of the model are taken into account, in order to ensure stability of the method for large time steps and simulation horizons. In the case of many layers, further efficiency can be gained by a layer reduction which is based on the vertical structure of fast and slow modes. Numerical experiments on the example of a mid-latitude regional ocean model confirm long term stability for time steps increased by an order of magnitude over the explicit CFL, while maintaining accuracy for key statistical quantities.