Up to 1920 processors of a cluster of distributed shared memory machines at the NASA Ames Research Center are being used to simulate ocean circulation globally at horizontal resolutions of 1/4, 1/8, and 1/16-degree with the Massachusetts Institute of Technology General Circulation Model, a finite volume code that can scale to large numbers of processors. The study aims to understand physical processes responsible for skill improvements as resolution is increased and to gain insight into what resolution is sufficient for particular purposes. This paper focuses on the computational aspects of reaching the technical objective of efficiently performing these global eddy-resolving ocean simulations. At 1/16-degree resolution the model grid contains 1.2 billion cells. At this resolution it is possible to simulate approximately one month of ocean dynamics in about 17 hours of wallclock time with a model timestep of two minutes on a cluster of four 512-way NUMA Altix systems. The Altix systems' large main memory and I/O subsystems allow computation and disk storage of rich sets of diagnostics during each integration, supporting the scientific objective to develop a better understanding of global ocean circulation model solution convergence as model resolution is increased.