A three dimensional differential field model for the spread of fire and smoke, on general orthogonal coordinate systems is developed. The model, which is designed for closed spaces, also includes the physical effects of turbulence, strong buoyancy, full compressibility, pressure rise due to fire loading, surface-surface and surface-flame radiation exchange, and heat losses through the wall. It is based on a control-volume staggered-cell finite- difference approach with primitive variables. Results of numerical calculations based on the field model are compared with test data for a methanol fire in the NRL FIRE I test facility which is in the form of a closed pressure vessel. Reasonable comparisons of the resulting pressure and temperatures at several locations have been obtained. Also shown are the detailed velocity and temperature fields inside the vessel at different time instants after the commencement of the fire. (mjm)