STABILITY ANALYSIS OF OPERATOR SPLITTING FOR LARGE-SCALE OCEAN MODELING

The ocean plays a crucial role in the earth's climate system, and an i mproved understanding of that role will be aided greatly by high-resol ution simulations of global ocean circulation over periods of many yea rs. For such simulations the computational requirements are extremely demanding and maximum efficiency is essential. However, the governing equations typically used for ocean modeling admit wave velocities havi ng widely varying magnitudes, and this situation can create serious pr oblems with the efficiency of numerical algorithms. One common approac h to resolving these problems is to split the fast and slow dynamics i nto separate subproblems. The fast motions are nearly independent of d epth, and it is natural to try to model these motions with a two-dimen sional system of equations. These fast equations could be solved with an implicit time discretization or with an explicit method with short time steps. The slow motions would then be modeled with a three-dimens ional system that is solved explicitly with long time steps that are d etermined by the slow wave speeds. However, if the splitting is inexac t, then the equations that model the slow motions might actually conta in some fast components, so the stability of explicit algorithms for t he slow equations could come into doubt. In this paper we discuss some general features of the operator splitting problem, and we then descr ibe an example of such a splitting and show that instability can arise in that case. (C) 1996 Academic Press, Inc.