For fast and effective simulation of filling processes of pressure vessels with compressed gaseous media, the governing equations are derived from a mass balance equation for the gas and from energy balance equations for the gas and the wall of the vessel. The gas is considered as a perfectly mixed phase and two heat transfer coefficients are introduced. The first one is the mean heat transfer coefficient between the gas and the inner surface of the pressure vessel, and the second one is the heat transfer coefficient between outer surface of the vessel and the surroundings. Because of the heat capacity of the wall of the pressure vessel, heat transfer from the compressed gas to the vessel wall strongly influences the temperature field of the gas. Until now no correlations have been available for the heat transfer coefficient between inflowing gas and inner surface of the vessel. To solve this problem, a computational fluid dynamics tool is used to determine the gas velocities at the vicinity of the inner surface of the vessel for a number of discrete surface elements. The results of a large amount of numerical experiments show that there exists a unique relationship between the gas velocity at the inlet and the tangential fluid velocities at the vicinity of the inner surface of the vessel for each vessel geometry. Once this unique relationship is known, the complete velocity distribution at the vicinity of the inner surface can be easily calculated from the inlet gas velocity. The near-wall velocities at the outer limit of the boundary layer are substituted into the heat transfer correlation for external flow over flat plates. The final heat transfer coefficient is the area-weighted mean of all local heat transfer coefficients. The method is applied to the special case of filling with hydrogen a 70-MPa composite vessel for fuel cell vehicles.