It is known that General Circulation Models (GCMs) have insufficient resolution to accurately simulate hurricane near-eye structure and intensity. The increasing capabilities of high-end computers have changed this. The mesoscale-resolving finite-volume GCM (fvGCM) has been experimentally deployed on the NASA Columbia supercomputer, and its performance is evaluated in this study by choosing hurricane Katrina as an example. In late August 2005, Katrina underwent two stages of rapid intensification, and became the sixth most intense hurricane in the Atlantic. Six 5-day simulations of Katrina at both 0.25° and 0.125° show comparable track forecasts but the 0.125° runs provide much better intensity forecasts, producing the center pressure with errors of only ±12 hPa. In the runs examined in this study, the 0.125° simulates better near-eye wind distributions and a more realistic average intensification rate. To contribute to the ongoing research on the effects of disabling convection parameterization (CP), we present promising results by comparing 0.125° runs with disabled CPs against runs with enabled CPs.