Simulation of two-phase flow is essential for nuclear industry as an important step towards a better design for safety and operation of nuclear reactors. This work aims at improving the accuracy and stability of current numerical schemes used in two-phase simulations, particularly two-fluid model used in ID system codes. Simulation results using a dissipative first-order accurate scheme, the Upwind Difference Scheme (UDS), will be presented. These will be compared to results using a second-order accurate scheme, the Linear Upwind Difference Scheme (LUDS). The dissipative and dispersive properties of the 1st and 2nd order schemes respectively will be studied using the modified equation analysis, and will be shown in numerical results for the faucet flow problem. A combination of the two schemes is applied using the flux limiter approach, where the 2nd order scheme is applied at smooth regions and dissipative 1st order scheme near discontinuities. Different limiters found in the literature are analyzed. For temporal discretization, the theta method is used.