Analytical models formulated to model accurately hydrogen transport in containments are presented. These models have been incorporated into the LIMIT computer code. The thermofluid dynamic model options span a wide range of applicability from rapid blowdown-type events to slow near-incompressible hydrogen injection. The utilization of distinct modeling treatments for the various accident stages is important, since the blowdown period is governed by thermofluid dynamic mechanisms (high Mach number, turbulent, multiphase forced convection), which are different from those of the postblowdown phase (low speed, multiphase, stratified natural convection). Detailed ancillary models of molecular and turbulent diffusion, mixture transport, and thermodynamic properties and heat sink modeling are addressed. The numerical solution of the governing equations is accomplished in discretizations of varying refinement, as are required for the successive stages of a containment accident, and emphasizes efficiency and accuracy. Two demonstration calculations are reported including the successful simulation of a large-scale experiment and the reproduction of an analytic result. Areas worthy of future development are also described. Overall, a versatile analysis methodology is introduced.