A dispersed how model a two-fluid model for a gas-liquid two-phase flow problem. This dispersed flow model is compared with a single pressure model used generally by adopting higher-order up-wind schemes for the advection terms. They are Kawamura-Kuwahara, UTOPIA, QUICK and the second order up-wind schemes. Analyses were carried out for a bubbly flow injected from a small circular central bottom wall of a cylindrical vessel. The computation for the dispersed flow model is more stable than the single pressure model. The QUICK scheme gives the best agreement with the measured results of the four schemes.