Unstructured C-Grid Discretization for Global Ocean Modeling 
G. R. Stuhne and W. R. Peltier 
gordan@atmosp.physics.utoronto.ca 

We have developed and tested novel unstructured-grid based methods
for oceanographic applications in embedded spherical geometry. The
numerical technology is based upon the marker-and-cell (MAC) scheme
on the Arakawa C-grid. Time-stepping is performed implicitly, and
the combined space-time discretization allows for the conservation of
linear and quadratic invariants. This eliminates the need for explicit
stabilization, which is an essential fixture in many higher-order
finite-element methods. Unstructured MAC schemes have been described
previously in the engineering and mathematical literature, but
global ocean modeling applications have led us to a number of original
contributions, including the derivation of the natural, energy-conserving
discretization for the Coriolis force term on the C-grid. As well as
discussing these technical issues, we will present and evaluate results
from oceanographic simulations using the new methods. 3-D hydrostatic
dynamics and shallow-water tidal dynamics have been successfully simulated
in spherical geometry. We are also working to incorporate sea-ice physics
and 3-D free-surface effects into the model, and results may be available
at the time of the workshop.